Contract Name:
AsteroidScans
Contract Source Code:
// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.7.6;
import "@openzeppelin/contracts/utils/Pausable.sol";
import "@openzeppelin/contracts/access/Ownable.sol";
import "./lib/InfluenceSettings.sol";
import "./lib/Procedural.sol";
import "./interfaces/IAsteroidToken.sol";
import "./interfaces/IAsteroidFeatures.sol";
/**
* @dev Contract that generates randomized perks based on when the asteroid is "scanned" by its owner. Perks
* are specific to certain types of asteroids, have varying degrees of rarity and can stack.
*/
contract AsteroidScans is Pausable, Ownable {
using Procedural for bytes32;
IAsteroidToken internal token;
IAsteroidFeatures internal features;
// Mapping indicating allowed managers
mapping (address => bool) private _managers;
/**
* @dev This is a bit-packed set of:
* << 0: the order purchased for scan boosts
* << 64: Bit-packed number with 15 bits. The first indicates whether the asteroid
* has been scanned, with the remainder pertaining to specific bonuses.
* << 128: The block number to use for the randomization hash
*/
mapping (uint => uint) internal scanInfo;
/**
* @dev Tracks the scan order to manage awarding early boosts to bonuses
*/
uint public scanOrderCount = 0;
event ScanStarted(uint indexed asteroidId);
event AsteroidScanned(uint indexed asteroidId, uint bonuses);
constructor(IAsteroidToken _token, IAsteroidFeatures _features) {
token = _token;
features = _features;
}
// Modifier to check if calling contract has the correct minting role
modifier onlyManagers {
require(isManager(_msgSender()), "Only managers can call this function");
_;
}
/**
* @dev Add a new account / contract that can mint / burn asteroids
* @param _manager Address of the new manager
*/
function addManager(address _manager) external onlyOwner {
_managers[_manager] = true;
}
/**
* @dev Remove a current manager
* @param _manager Address of the manager to be removed
*/
function removeManager(address _manager) external onlyOwner {
_managers[_manager] = false;
}
/**
* @dev Checks if an address is a manager
* @param _manager Address of contract / account to check
*/
function isManager(address _manager) public view returns (bool) {
return _managers[_manager];
}
/**
* @dev Sets the order the asteroid should receive boosts to bonuses
* @param _asteroidId The ERC721 token ID of the asteroid
*/
function recordScanOrder(uint _asteroidId) external onlyManagers {
scanOrderCount += 1;
scanInfo[_asteroidId] = scanOrderCount;
}
/**
* @dev Returns the scan order for managing boosts for a particular asteroid
* @param _asteroidId The ERC721 token ID of the asteroid
*/
function getScanOrder(uint _asteroidId) external view returns(uint) {
return uint(uint64(scanInfo[_asteroidId]));
}
/**
* @dev Method to pre-scan a set of asteroids to be offered during pre-sale. This method may only be run
* before any sale purchases have been made.
* @param _asteroidIds An array of asteroid ERC721 token IDs
* @param _bonuses An array of bit-packed bonuses corresponding to _asteroidIds
*/
function setInitialBonuses(uint[] calldata _asteroidIds, uint[] calldata _bonuses) external onlyOwner {
require(scanOrderCount == 0);
require(_asteroidIds.length == _bonuses.length);
for (uint i = 0; i < _asteroidIds.length; i++) {
scanInfo[_asteroidIds[i]] |= _bonuses[i] << 64;
emit AsteroidScanned(_asteroidIds[i], _bonuses[i]);
}
}
/**
* @dev Starts the scan and defines the future blockhash to use for
* @param _asteroidId The ERC721 token ID of the asteroid
*/
function startScan(uint _asteroidId) external whenNotPaused {
require(token.ownerOf(_asteroidId) == _msgSender(), "Only owner can scan asteroid");
require(uint(uint64(scanInfo[_asteroidId] >> 64)) == 0, "Asteroid has already been scanned");
require(uint(uint64(scanInfo[_asteroidId] >> 128)) == 0, "Asteroid scanning has already started");
scanInfo[_asteroidId] |= (block.number + 1) << 128;
emit ScanStarted(_asteroidId);
}
/**
* @dev Returns a set of 0 or more perks for the asteroid randomized by time / owner address
* @param _asteroidId The ERC721 token ID of the asteroid
*/
function finalizeScan(uint _asteroidId) external whenNotPaused {
uint blockForHash = uint(uint64(scanInfo[_asteroidId] >> 128));
require(uint(uint64(scanInfo[_asteroidId] >> 64)) == 0, "Asteroid has already been scanned");
require(blockForHash != block.number && blockForHash > 0, "Must wait at least one block after starting");
// Capture the bonuses bitpacked into a uint. The first bit is set to indicate the asteroid has been scanned.
uint bonuses = 1;
uint purchaseOrder = uint(uint64(scanInfo[_asteroidId]));
uint bonusTest;
bytes32 seed = features.getAsteroidSeed(_asteroidId);
uint spectralType = features.getSpectralTypeBySeed(seed);
// Add some randomness to the bonuses outcome
uint bhash = uint(blockhash(blockForHash));
// bhash == 0 if we're later than 256 blocks after startScan, this will default to no bonus
if (bhash != 0) {
seed = seed.derive(bhash);
// Array of possible bonuses (0 or 1) per spectral type (same order as spectral types in AsteroidFeatures)
uint8[6][11] memory bonusRates = [
[ 1, 1, 0, 1, 0, 0 ],
[ 1, 1, 1, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0 ],
[ 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1 ],
[ 1, 0, 1, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 1 ],
[ 1, 1, 1, 0, 1, 1 ],
[ 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 0, 0, 0, 0 ]
];
// Boosts the bonus chances based on early scan tranches
int128 rollMax = 10001;
if (purchaseOrder < 100) {
rollMax = 3441; // 4x increase
} else if (purchaseOrder < 1100) {
rollMax = 4143; // 3x increase
} else if (purchaseOrder < 11100) {
rollMax = 5588; // 2x increase
}
// Loop over the possible bonuses for the spectral class
for (uint i = 0; i < 6; i++) {
// Handles the case for regular bonuses
if (i < 4 && bonusRates[spectralType][i] == 1) {
bonusTest = uint(seed.derive(i).getIntBetween(0, rollMax));
if (bonusTest <= 2100) {
if (bonusTest > 600) {
bonuses = bonuses | (1 << (i * 3 + 1)); // Tier 1 regular bonus (15% of asteroids)
} else if (bonusTest > 100) {
bonuses = bonuses | (1 << (i * 3 + 2)); // Tier 2 regular bonus (5% of asteroids)
} else {
bonuses = bonuses | (1 << (i * 3 + 3)); // Tier 3 regular bonus (1% of asteroids)
}
}
}
// Handle the case for the special bonuses
if (i >= 4 && bonusRates[spectralType][i] == 1) {
bonusTest = uint(seed.derive(i).getIntBetween(0, rollMax));
if (bonusTest <= 250) {
bonuses = bonuses | (1 << (i + 9)); // Single tier special bonus (2.5% of asteroids)
}
}
}
// Guarantees at least a level 1 yield bonus for the early adopters
if (purchaseOrder < 11100 && bonuses == 1) {
bonuses = 3;
}
}
scanInfo[_asteroidId] |= bonuses << 64;
emit AsteroidScanned(_asteroidId, bonuses);
}
/**
* @dev Query for the results of an asteroid scan
* @param _asteroidId The ERC721 token ID of the asteroid
*/
function retrieveScan(uint _asteroidId) external view returns (uint) {
return uint(uint64(scanInfo[_asteroidId] >> 64));
}
}
// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.7.6;
interface IAsteroidFeatures {
function getAsteroidSeed(uint _asteroidId) external pure returns (bytes32);
function getRadius(uint _asteroidId) external pure returns (uint);
function getSpectralType(uint _asteroidId) external pure returns (uint);
function getSpectralTypeBySeed(bytes32 _seed) external pure returns (uint);
function getOrbitalElements(uint _asteroidId) external pure returns (uint[6] memory orbitalElements);
function getOrbitalElementsBySeed(bytes32 _seed) external pure returns (uint[6] memory orbitalElements);
}
// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.7.6;
import "@openzeppelin/contracts/token/ERC721/IERC721.sol";
interface IAsteroidToken is IERC721 {
function addManager(address _manager) external;
function removeManager(address _manager) external;
function isManager(address _manager) external view returns (bool);
function mint(address _to, uint256 _tokenId) external;
function burn(address _owner, uint256 _tokenId) external;
}
// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.7.0;
library InfluenceSettings {
// Game constants
bytes32 public constant MASTER_SEED = "influence";
uint32 public constant MAX_RADIUS = 375142; // in meters
uint32 public constant START_TIMESTAMP = 1609459200; // Zero date timestamp for orbits
uint public constant TOTAL_ASTEROIDS = 250000;
}
// SPDX-License-Identifier: UNLICENSED
// Portions licensed under NovakDistribute license (ref LICENSE file)
pragma solidity ^0.7.0;
import "abdk-libraries-solidity/ABDKMath64x64.sol";
library Procedural {
using ABDKMath64x64 for *;
/**
* @dev Mix string data into a hash and return a new one.
*/
function derive(bytes32 _self, string memory _entropy) public pure returns (bytes32) {
return sha256(abi.encodePacked(_self, _entropy));
}
/**
* @dev Mix signed int data into a hash and return a new one.
*/
function derive(bytes32 _self, int256 _entropy) public pure returns (bytes32) {
return sha256(abi.encodePacked(_self, _entropy));
}
/**
* @dev Mix unsigned int data into a hash and return a new one.
*/
function derive(bytes32 _self, uint _entropy) public pure returns (bytes32) {
return sha256(abi.encodePacked(_self, _entropy));
}
/**
* @dev Returns the base pseudorandom hash for the given RandNode. Does another round of hashing
* in case an un-encoded string was passed.
*/
function getHash(bytes32 _self) public pure returns (bytes32) {
return sha256(abi.encodePacked(_self));
}
/**
* @dev Get an int128 full of random bits.
*/
function getInt128(bytes32 _self) public pure returns (int128) {
return int128(int256(getHash(_self)));
}
/**
* @dev Get a 64.64 fixed point (see ABDK math) where: 0 <= return value < 1
*/
function getReal(bytes32 _self) public pure returns (int128) {
int128 fixedOne = int128(1 << 64);
return getInt128(_self).abs() % fixedOne;
}
/**
* @dev Get an integer between low, inclusive, and high, exclusive. Represented as a normal int, not a real.
*/
function getIntBetween(bytes32 _self, int128 _low, int128 _high) public pure returns (int64) {
_low = _low.fromInt();
_high = _high.fromInt();
int128 range = _high.sub(_low);
int128 result = getReal(_self).mul(range).add(_low);
return result.toInt();
}
/**
* @dev Returns a normal int (roughly) normally distributed value between low and high
*/
function getNormalIntBetween(bytes32 _self, int128 _low, int128 _high) public pure returns (int64) {
int128 accumulator = 0;
for (uint i = 0; i < 5; i++) {
accumulator += getIntBetween(derive(_self, i), _low, _high);
}
return accumulator.fromInt().div(5.fromUInt()).toInt();
}
/**
* @dev "Folds" a normal int distribution in half to generate an approx decay function
* Only takes a high value (exclusive) as the simplistic approximation relies on low being zero
* Returns a normal int, not a real
*/
function getDecayingIntBelow(bytes32 _self, uint _high) public pure returns (int64) {
require(_high < uint(1 << 64));
int64 normalInt = getNormalIntBetween(_self, 0, int128(_high * 2 - 1));
int128 adjusted = int128(normalInt) - int128(_high);
return adjusted.fromInt().abs().toInt();
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.6.0 <0.8.0;
import "../utils/Context.sol";
/**
* @dev Contract module which provides a basic access control mechanism, where
* there is an account (an owner) that can be granted exclusive access to
* specific functions.
*
* By default, the owner account will be the one that deploys the contract. This
* can later be changed with {transferOwnership}.
*
* This module is used through inheritance. It will make available the modifier
* `onlyOwner`, which can be applied to your functions to restrict their use to
* the owner.
*/
abstract contract Ownable is Context {
address private _owner;
event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
/**
* @dev Initializes the contract setting the deployer as the initial owner.
*/
constructor () internal {
address msgSender = _msgSender();
_owner = msgSender;
emit OwnershipTransferred(address(0), msgSender);
}
/**
* @dev Returns the address of the current owner.
*/
function owner() public view virtual returns (address) {
return _owner;
}
/**
* @dev Throws if called by any account other than the owner.
*/
modifier onlyOwner() {
require(owner() == _msgSender(), "Ownable: caller is not the owner");
_;
}
/**
* @dev Leaves the contract without owner. It will not be possible to call
* `onlyOwner` functions anymore. Can only be called by the current owner.
*
* NOTE: Renouncing ownership will leave the contract without an owner,
* thereby removing any functionality that is only available to the owner.
*/
function renounceOwnership() public virtual onlyOwner {
emit OwnershipTransferred(_owner, address(0));
_owner = address(0);
}
/**
* @dev Transfers ownership of the contract to a new account (`newOwner`).
* Can only be called by the current owner.
*/
function transferOwnership(address newOwner) public virtual onlyOwner {
require(newOwner != address(0), "Ownable: new owner is the zero address");
emit OwnershipTransferred(_owner, newOwner);
_owner = newOwner;
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.6.0 <0.8.0;
/**
* @dev Interface of the ERC165 standard, as defined in the
* https://eips.ethereum.org/EIPS/eip-165[EIP].
*
* Implementers can declare support of contract interfaces, which can then be
* queried by others ({ERC165Checker}).
*
* For an implementation, see {ERC165}.
*/
interface IERC165 {
/**
* @dev Returns true if this contract implements the interface defined by
* `interfaceId`. See the corresponding
* https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
* to learn more about how these ids are created.
*
* This function call must use less than 30 000 gas.
*/
function supportsInterface(bytes4 interfaceId) external view returns (bool);
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.6.2 <0.8.0;
import "../../introspection/IERC165.sol";
/**
* @dev Required interface of an ERC721 compliant contract.
*/
interface IERC721 is IERC165 {
/**
* @dev Emitted when `tokenId` token is transferred from `from` to `to`.
*/
event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);
/**
* @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
*/
event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);
/**
* @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
*/
event ApprovalForAll(address indexed owner, address indexed operator, bool approved);
/**
* @dev Returns the number of tokens in ``owner``'s account.
*/
function balanceOf(address owner) external view returns (uint256 balance);
/**
* @dev Returns the owner of the `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function ownerOf(uint256 tokenId) external view returns (address owner);
/**
* @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
* are aware of the ERC721 protocol to prevent tokens from being forever locked.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must exist and be owned by `from`.
* - If the caller is not `from`, it must be have been allowed to move this token by either {approve} or {setApprovalForAll}.
* - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
*
* Emits a {Transfer} event.
*/
function safeTransferFrom(address from, address to, uint256 tokenId) external;
/**
* @dev Transfers `tokenId` token from `from` to `to`.
*
* WARNING: Usage of this method is discouraged, use {safeTransferFrom} whenever possible.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must be owned by `from`.
* - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
*
* Emits a {Transfer} event.
*/
function transferFrom(address from, address to, uint256 tokenId) external;
/**
* @dev Gives permission to `to` to transfer `tokenId` token to another account.
* The approval is cleared when the token is transferred.
*
* Only a single account can be approved at a time, so approving the zero address clears previous approvals.
*
* Requirements:
*
* - The caller must own the token or be an approved operator.
* - `tokenId` must exist.
*
* Emits an {Approval} event.
*/
function approve(address to, uint256 tokenId) external;
/**
* @dev Returns the account approved for `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function getApproved(uint256 tokenId) external view returns (address operator);
/**
* @dev Approve or remove `operator` as an operator for the caller.
* Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
*
* Requirements:
*
* - The `operator` cannot be the caller.
*
* Emits an {ApprovalForAll} event.
*/
function setApprovalForAll(address operator, bool _approved) external;
/**
* @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
*
* See {setApprovalForAll}
*/
function isApprovedForAll(address owner, address operator) external view returns (bool);
/**
* @dev Safely transfers `tokenId` token from `from` to `to`.
*
* Requirements:
*
* - `from` cannot be the zero address.
* - `to` cannot be the zero address.
* - `tokenId` token must exist and be owned by `from`.
* - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
* - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
*
* Emits a {Transfer} event.
*/
function safeTransferFrom(address from, address to, uint256 tokenId, bytes calldata data) external;
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.6.0 <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 GSN meta-transactions the account sending and
* paying for execution may not be the actual sender (as far as an application
* is concerned).
*
* This contract is only required for intermediate, library-like contracts.
*/
abstract contract Context {
function _msgSender() internal view virtual returns (address payable) {
return msg.sender;
}
function _msgData() internal view virtual returns (bytes memory) {
this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
return msg.data;
}
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.6.0 <0.8.0;
import "./Context.sol";
/**
* @dev Contract module which allows children to implement an emergency stop
* mechanism that can be triggered by an authorized account.
*
* This module is used through inheritance. It will make available the
* modifiers `whenNotPaused` and `whenPaused`, which can be applied to
* the functions of your contract. Note that they will not be pausable by
* simply including this module, only once the modifiers are put in place.
*/
abstract contract Pausable is Context {
/**
* @dev Emitted when the pause is triggered by `account`.
*/
event Paused(address account);
/**
* @dev Emitted when the pause is lifted by `account`.
*/
event Unpaused(address account);
bool private _paused;
/**
* @dev Initializes the contract in unpaused state.
*/
constructor () internal {
_paused = false;
}
/**
* @dev Returns true if the contract is paused, and false otherwise.
*/
function paused() public view virtual returns (bool) {
return _paused;
}
/**
* @dev Modifier to make a function callable only when the contract is not paused.
*
* Requirements:
*
* - The contract must not be paused.
*/
modifier whenNotPaused() {
require(!paused(), "Pausable: paused");
_;
}
/**
* @dev Modifier to make a function callable only when the contract is paused.
*
* Requirements:
*
* - The contract must be paused.
*/
modifier whenPaused() {
require(paused(), "Pausable: not paused");
_;
}
/**
* @dev Triggers stopped state.
*
* Requirements:
*
* - The contract must not be paused.
*/
function _pause() internal virtual whenNotPaused {
_paused = true;
emit Paused(_msgSender());
}
/**
* @dev Returns to normal state.
*
* Requirements:
*
* - The contract must be paused.
*/
function _unpause() internal virtual whenPaused {
_paused = false;
emit Unpaused(_msgSender());
}
}
// SPDX-License-Identifier: BSD-4-Clause
/*
* ABDK Math 64.64 Smart Contract Library. Copyright © 2019 by ABDK Consulting.
* Author: Mikhail Vladimirov <[email protected]>
*/
pragma solidity ^0.5.0 || ^0.6.0 || ^0.7.0;
/**
* Smart contract library of mathematical functions operating with signed
* 64.64-bit fixed point numbers. Signed 64.64-bit fixed point number is
* basically a simple fraction whose numerator is signed 128-bit integer and
* denominator is 2^64. As long as denominator is always the same, there is no
* need to store it, thus in Solidity signed 64.64-bit fixed point numbers are
* represented by int128 type holding only the numerator.
*/
library ABDKMath64x64 {
/*
* Minimum value signed 64.64-bit fixed point number may have.
*/
int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;
/*
* Maximum value signed 64.64-bit fixed point number may have.
*/
int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
/**
* Convert signed 256-bit integer number into signed 64.64-bit fixed point
* number. Revert on overflow.
*
* @param x signed 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function fromInt (int256 x) internal pure returns (int128) {
require (x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF);
return int128 (x << 64);
}
/**
* Convert signed 64.64 fixed point number into signed 64-bit integer number
* rounding down.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64-bit integer number
*/
function toInt (int128 x) internal pure returns (int64) {
return int64 (x >> 64);
}
/**
* Convert unsigned 256-bit integer number into signed 64.64-bit fixed point
* number. Revert on overflow.
*
* @param x unsigned 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function fromUInt (uint256 x) internal pure returns (int128) {
require (x <= 0x7FFFFFFFFFFFFFFF);
return int128 (x << 64);
}
/**
* Convert signed 64.64 fixed point number into unsigned 64-bit integer
* number rounding down. Revert on underflow.
*
* @param x signed 64.64-bit fixed point number
* @return unsigned 64-bit integer number
*/
function toUInt (int128 x) internal pure returns (uint64) {
require (x >= 0);
return uint64 (x >> 64);
}
/**
* Convert signed 128.128 fixed point number into signed 64.64-bit fixed point
* number rounding down. Revert on overflow.
*
* @param x signed 128.128-bin fixed point number
* @return signed 64.64-bit fixed point number
*/
function from128x128 (int256 x) internal pure returns (int128) {
int256 result = x >> 64;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
/**
* Convert signed 64.64 fixed point number into signed 128.128 fixed point
* number.
*
* @param x signed 64.64-bit fixed point number
* @return signed 128.128 fixed point number
*/
function to128x128 (int128 x) internal pure returns (int256) {
return int256 (x) << 64;
}
/**
* Calculate x + y. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function add (int128 x, int128 y) internal pure returns (int128) {
int256 result = int256(x) + y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
/**
* Calculate x - y. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function sub (int128 x, int128 y) internal pure returns (int128) {
int256 result = int256(x) - y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
/**
* Calculate x * y rounding down. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function mul (int128 x, int128 y) internal pure returns (int128) {
int256 result = int256(x) * y >> 64;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
/**
* Calculate x * y rounding towards zero, where x is signed 64.64 fixed point
* number and y is signed 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64 fixed point number
* @param y signed 256-bit integer number
* @return signed 256-bit integer number
*/
function muli (int128 x, int256 y) internal pure returns (int256) {
if (x == MIN_64x64) {
require (y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF &&
y <= 0x1000000000000000000000000000000000000000000000000);
return -y << 63;
} else {
bool negativeResult = false;
if (x < 0) {
x = -x;
negativeResult = true;
}
if (y < 0) {
y = -y; // We rely on overflow behavior here
negativeResult = !negativeResult;
}
uint256 absoluteResult = mulu (x, uint256 (y));
if (negativeResult) {
require (absoluteResult <=
0x8000000000000000000000000000000000000000000000000000000000000000);
return -int256 (absoluteResult); // We rely on overflow behavior here
} else {
require (absoluteResult <=
0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return int256 (absoluteResult);
}
}
}
/**
* Calculate x * y rounding down, where x is signed 64.64 fixed point number
* and y is unsigned 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64 fixed point number
* @param y unsigned 256-bit integer number
* @return unsigned 256-bit integer number
*/
function mulu (int128 x, uint256 y) internal pure returns (uint256) {
if (y == 0) return 0;
require (x >= 0);
uint256 lo = (uint256 (x) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;
uint256 hi = uint256 (x) * (y >> 128);
require (hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
hi <<= 64;
require (hi <=
0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - lo);
return hi + lo;
}
/**
* Calculate x / y rounding towards zero. Revert on overflow or when y is
* zero.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function div (int128 x, int128 y) internal pure returns (int128) {
require (y != 0);
int256 result = (int256 (x) << 64) / y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
/**
* Calculate x / y rounding towards zero, where x and y are signed 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x signed 256-bit integer number
* @param y signed 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function divi (int256 x, int256 y) internal pure returns (int128) {
require (y != 0);
bool negativeResult = false;
if (x < 0) {
x = -x; // We rely on overflow behavior here
negativeResult = true;
}
if (y < 0) {
y = -y; // We rely on overflow behavior here
negativeResult = !negativeResult;
}
uint128 absoluteResult = divuu (uint256 (x), uint256 (y));
if (negativeResult) {
require (absoluteResult <= 0x80000000000000000000000000000000);
return -int128 (absoluteResult); // We rely on overflow behavior here
} else {
require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return int128 (absoluteResult); // We rely on overflow behavior here
}
}
/**
* Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x unsigned 256-bit integer number
* @param y unsigned 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function divu (uint256 x, uint256 y) internal pure returns (int128) {
require (y != 0);
uint128 result = divuu (x, y);
require (result <= uint128 (MAX_64x64));
return int128 (result);
}
/**
* Calculate -x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function neg (int128 x) internal pure returns (int128) {
require (x != MIN_64x64);
return -x;
}
/**
* Calculate |x|. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function abs (int128 x) internal pure returns (int128) {
require (x != MIN_64x64);
return x < 0 ? -x : x;
}
/**
* Calculate 1 / x rounding towards zero. Revert on overflow or when x is
* zero.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function inv (int128 x) internal pure returns (int128) {
require (x != 0);
int256 result = int256 (0x100000000000000000000000000000000) / x;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
/**
* Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function avg (int128 x, int128 y) internal pure returns (int128) {
return int128 ((int256 (x) + int256 (y)) >> 1);
}
/**
* Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down.
* Revert on overflow or in case x * y is negative.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function gavg (int128 x, int128 y) internal pure returns (int128) {
int256 m = int256 (x) * int256 (y);
require (m >= 0);
require (m <
0x4000000000000000000000000000000000000000000000000000000000000000);
return int128 (sqrtu (uint256 (m)));
}
/**
* Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number
* and y is unsigned 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y uint256 value
* @return signed 64.64-bit fixed point number
*/
function pow (int128 x, uint256 y) internal pure returns (int128) {
uint256 absoluteResult;
bool negativeResult = false;
if (x >= 0) {
absoluteResult = powu (uint256 (x) << 63, y);
} else {
// We rely on overflow behavior here
absoluteResult = powu (uint256 (uint128 (-x)) << 63, y);
negativeResult = y & 1 > 0;
}
absoluteResult >>= 63;
if (negativeResult) {
require (absoluteResult <= 0x80000000000000000000000000000000);
return -int128 (absoluteResult); // We rely on overflow behavior here
} else {
require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return int128 (absoluteResult); // We rely on overflow behavior here
}
}
/**
* Calculate sqrt (x) rounding down. Revert if x < 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function sqrt (int128 x) internal pure returns (int128) {
require (x >= 0);
return int128 (sqrtu (uint256 (x) << 64));
}
/**
* Calculate binary logarithm of x. Revert if x <= 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function log_2 (int128 x) internal pure returns (int128) {
require (x > 0);
int256 msb = 0;
int256 xc = x;
if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; }
if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
if (xc >= 0x10000) { xc >>= 16; msb += 16; }
if (xc >= 0x100) { xc >>= 8; msb += 8; }
if (xc >= 0x10) { xc >>= 4; msb += 4; }
if (xc >= 0x4) { xc >>= 2; msb += 2; }
if (xc >= 0x2) msb += 1; // No need to shift xc anymore
int256 result = msb - 64 << 64;
uint256 ux = uint256 (x) << uint256 (127 - msb);
for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) {
ux *= ux;
uint256 b = ux >> 255;
ux >>= 127 + b;
result += bit * int256 (b);
}
return int128 (result);
}
/**
* Calculate natural logarithm of x. Revert if x <= 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function ln (int128 x) internal pure returns (int128) {
require (x > 0);
return int128 (
uint256 (log_2 (x)) * 0xB17217F7D1CF79ABC9E3B39803F2F6AF >> 128);
}
/**
* Calculate binary exponent of x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function exp_2 (int128 x) internal pure returns (int128) {
require (x < 0x400000000000000000); // Overflow
if (x < -0x400000000000000000) return 0; // Underflow
uint256 result = 0x80000000000000000000000000000000;
if (x & 0x8000000000000000 > 0)
result = result * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128;
if (x & 0x4000000000000000 > 0)
result = result * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128;
if (x & 0x2000000000000000 > 0)
result = result * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128;
if (x & 0x1000000000000000 > 0)
result = result * 0x10B5586CF9890F6298B92B71842A98363 >> 128;
if (x & 0x800000000000000 > 0)
result = result * 0x1059B0D31585743AE7C548EB68CA417FD >> 128;
if (x & 0x400000000000000 > 0)
result = result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128;
if (x & 0x200000000000000 > 0)
result = result * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128;
if (x & 0x100000000000000 > 0)
result = result * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128;
if (x & 0x80000000000000 > 0)
result = result * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128;
if (x & 0x40000000000000 > 0)
result = result * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128;
if (x & 0x20000000000000 > 0)
result = result * 0x100162F3904051FA128BCA9C55C31E5DF >> 128;
if (x & 0x10000000000000 > 0)
result = result * 0x1000B175EFFDC76BA38E31671CA939725 >> 128;
if (x & 0x8000000000000 > 0)
result = result * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128;
if (x & 0x4000000000000 > 0)
result = result * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128;
if (x & 0x2000000000000 > 0)
result = result * 0x1000162E525EE054754457D5995292026 >> 128;
if (x & 0x1000000000000 > 0)
result = result * 0x10000B17255775C040618BF4A4ADE83FC >> 128;
if (x & 0x800000000000 > 0)
result = result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128;
if (x & 0x400000000000 > 0)
result = result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128;
if (x & 0x200000000000 > 0)
result = result * 0x10000162E43F4F831060E02D839A9D16D >> 128;
if (x & 0x100000000000 > 0)
result = result * 0x100000B1721BCFC99D9F890EA06911763 >> 128;
if (x & 0x80000000000 > 0)
result = result * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128;
if (x & 0x40000000000 > 0)
result = result * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128;
if (x & 0x20000000000 > 0)
result = result * 0x100000162E430E5A18F6119E3C02282A5 >> 128;
if (x & 0x10000000000 > 0)
result = result * 0x1000000B1721835514B86E6D96EFD1BFE >> 128;
if (x & 0x8000000000 > 0)
result = result * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128;
if (x & 0x4000000000 > 0)
result = result * 0x10000002C5C8601CC6B9E94213C72737A >> 128;
if (x & 0x2000000000 > 0)
result = result * 0x1000000162E42FFF037DF38AA2B219F06 >> 128;
if (x & 0x1000000000 > 0)
result = result * 0x10000000B17217FBA9C739AA5819F44F9 >> 128;
if (x & 0x800000000 > 0)
result = result * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128;
if (x & 0x400000000 > 0)
result = result * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128;
if (x & 0x200000000 > 0)
result = result * 0x10000000162E42FF0999CE3541B9FFFCF >> 128;
if (x & 0x100000000 > 0)
result = result * 0x100000000B17217F80F4EF5AADDA45554 >> 128;
if (x & 0x80000000 > 0)
result = result * 0x10000000058B90BFBF8479BD5A81B51AD >> 128;
if (x & 0x40000000 > 0)
result = result * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128;
if (x & 0x20000000 > 0)
result = result * 0x100000000162E42FEFB2FED257559BDAA >> 128;
if (x & 0x10000000 > 0)
result = result * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128;
if (x & 0x8000000 > 0)
result = result * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128;
if (x & 0x4000000 > 0)
result = result * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128;
if (x & 0x2000000 > 0)
result = result * 0x1000000000162E42FEFA494F1478FDE05 >> 128;
if (x & 0x1000000 > 0)
result = result * 0x10000000000B17217F7D20CF927C8E94C >> 128;
if (x & 0x800000 > 0)
result = result * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128;
if (x & 0x400000 > 0)
result = result * 0x100000000002C5C85FDF477B662B26945 >> 128;
if (x & 0x200000 > 0)
result = result * 0x10000000000162E42FEFA3AE53369388C >> 128;
if (x & 0x100000 > 0)
result = result * 0x100000000000B17217F7D1D351A389D40 >> 128;
if (x & 0x80000 > 0)
result = result * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128;
if (x & 0x40000 > 0)
result = result * 0x1000000000002C5C85FDF4741BEA6E77E >> 128;
if (x & 0x20000 > 0)
result = result * 0x100000000000162E42FEFA39FE95583C2 >> 128;
if (x & 0x10000 > 0)
result = result * 0x1000000000000B17217F7D1CFB72B45E1 >> 128;
if (x & 0x8000 > 0)
result = result * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128;
if (x & 0x4000 > 0)
result = result * 0x10000000000002C5C85FDF473E242EA38 >> 128;
if (x & 0x2000 > 0)
result = result * 0x1000000000000162E42FEFA39F02B772C >> 128;
if (x & 0x1000 > 0)
result = result * 0x10000000000000B17217F7D1CF7D83C1A >> 128;
if (x & 0x800 > 0)
result = result * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128;
if (x & 0x400 > 0)
result = result * 0x100000000000002C5C85FDF473DEA871F >> 128;
if (x & 0x200 > 0)
result = result * 0x10000000000000162E42FEFA39EF44D91 >> 128;
if (x & 0x100 > 0)
result = result * 0x100000000000000B17217F7D1CF79E949 >> 128;
if (x & 0x80 > 0)
result = result * 0x10000000000000058B90BFBE8E7BCE544 >> 128;
if (x & 0x40 > 0)
result = result * 0x1000000000000002C5C85FDF473DE6ECA >> 128;
if (x & 0x20 > 0)
result = result * 0x100000000000000162E42FEFA39EF366F >> 128;
if (x & 0x10 > 0)
result = result * 0x1000000000000000B17217F7D1CF79AFA >> 128;
if (x & 0x8 > 0)
result = result * 0x100000000000000058B90BFBE8E7BCD6D >> 128;
if (x & 0x4 > 0)
result = result * 0x10000000000000002C5C85FDF473DE6B2 >> 128;
if (x & 0x2 > 0)
result = result * 0x1000000000000000162E42FEFA39EF358 >> 128;
if (x & 0x1 > 0)
result = result * 0x10000000000000000B17217F7D1CF79AB >> 128;
result >>= uint256 (63 - (x >> 64));
require (result <= uint256 (MAX_64x64));
return int128 (result);
}
/**
* Calculate natural exponent of x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function exp (int128 x) internal pure returns (int128) {
require (x < 0x400000000000000000); // Overflow
if (x < -0x400000000000000000) return 0; // Underflow
return exp_2 (
int128 (int256 (x) * 0x171547652B82FE1777D0FFDA0D23A7D12 >> 128));
}
/**
* Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x unsigned 256-bit integer number
* @param y unsigned 256-bit integer number
* @return unsigned 64.64-bit fixed point number
*/
function divuu (uint256 x, uint256 y) private pure returns (uint128) {
require (y != 0);
uint256 result;
if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
result = (x << 64) / y;
else {
uint256 msb = 192;
uint256 xc = x >> 192;
if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
if (xc >= 0x10000) { xc >>= 16; msb += 16; }
if (xc >= 0x100) { xc >>= 8; msb += 8; }
if (xc >= 0x10) { xc >>= 4; msb += 4; }
if (xc >= 0x4) { xc >>= 2; msb += 2; }
if (xc >= 0x2) msb += 1; // No need to shift xc anymore
result = (x << 255 - msb) / ((y - 1 >> msb - 191) + 1);
require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
uint256 hi = result * (y >> 128);
uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
uint256 xh = x >> 192;
uint256 xl = x << 64;
if (xl < lo) xh -= 1;
xl -= lo; // We rely on overflow behavior here
lo = hi << 128;
if (xl < lo) xh -= 1;
xl -= lo; // We rely on overflow behavior here
assert (xh == hi >> 128);
result += xl / y;
}
require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return uint128 (result);
}
/**
* Calculate x^y assuming 0^0 is 1, where x is unsigned 129.127 fixed point
* number and y is unsigned 256-bit integer number. Revert on overflow.
*
* @param x unsigned 129.127-bit fixed point number
* @param y uint256 value
* @return unsigned 129.127-bit fixed point number
*/
function powu (uint256 x, uint256 y) private pure returns (uint256) {
if (y == 0) return 0x80000000000000000000000000000000;
else if (x == 0) return 0;
else {
int256 msb = 0;
uint256 xc = x;
if (xc >= 0x100000000000000000000000000000000) { xc >>= 128; msb += 128; }
if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; }
if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
if (xc >= 0x10000) { xc >>= 16; msb += 16; }
if (xc >= 0x100) { xc >>= 8; msb += 8; }
if (xc >= 0x10) { xc >>= 4; msb += 4; }
if (xc >= 0x4) { xc >>= 2; msb += 2; }
if (xc >= 0x2) msb += 1; // No need to shift xc anymore
int256 xe = msb - 127;
if (xe > 0) x >>= uint256 (xe);
else x <<= uint256 (-xe);
uint256 result = 0x80000000000000000000000000000000;
int256 re = 0;
while (y > 0) {
if (y & 1 > 0) {
result = result * x;
y -= 1;
re += xe;
if (result >=
0x8000000000000000000000000000000000000000000000000000000000000000) {
result >>= 128;
re += 1;
} else result >>= 127;
if (re < -127) return 0; // Underflow
require (re < 128); // Overflow
} else {
x = x * x;
y >>= 1;
xe <<= 1;
if (x >=
0x8000000000000000000000000000000000000000000000000000000000000000) {
x >>= 128;
xe += 1;
} else x >>= 127;
if (xe < -127) return 0; // Underflow
require (xe < 128); // Overflow
}
}
if (re > 0) result <<= uint256 (re);
else if (re < 0) result >>= uint256 (-re);
return result;
}
}
/**
* Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer
* number.
*
* @param x unsigned 256-bit integer number
* @return unsigned 128-bit integer number
*/
function sqrtu (uint256 x) private pure returns (uint128) {
if (x == 0) return 0;
else {
uint256 xx = x;
uint256 r = 1;
if (xx >= 0x100000000000000000000000000000000) { xx >>= 128; r <<= 64; }
if (xx >= 0x10000000000000000) { xx >>= 64; r <<= 32; }
if (xx >= 0x100000000) { xx >>= 32; r <<= 16; }
if (xx >= 0x10000) { xx >>= 16; r <<= 8; }
if (xx >= 0x100) { xx >>= 8; r <<= 4; }
if (xx >= 0x10) { xx >>= 4; r <<= 2; }
if (xx >= 0x8) { r <<= 1; }
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1; // Seven iterations should be enough
uint256 r1 = x / r;
return uint128 (r < r1 ? r : r1);
}
}
}