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Contract Source Code Verified (Exact Match)
Contract Name:
SablierV2NFTDescriptor
Compiler Version
v0.8.26+commit.8a97fa7a
ZkSolc Version
v1.5.1
Optimization Enabled:
Yes with Mode z
Other Settings:
paris EvmVersion
Contract Source Code (Solidity Standard Json-Input format)
// SPDX-License-Identifier: GPL-3.0-or-later
// solhint-disable max-line-length,quotes
pragma solidity >=0.8.22;
import { IERC20Metadata } from "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import { IERC721Metadata } from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
import { Base64 } from "@openzeppelin/contracts/utils/Base64.sol";
import { Strings } from "@openzeppelin/contracts/utils/Strings.sol";
import { ISablierV2Lockup } from "./interfaces/ISablierV2Lockup.sol";
import { ISablierV2NFTDescriptor } from "./interfaces/ISablierV2NFTDescriptor.sol";
import { Lockup } from "./types/DataTypes.sol";
import { Errors } from "./libraries/Errors.sol";
import { NFTSVG } from "./libraries/NFTSVG.sol";
import { SVGElements } from "./libraries/SVGElements.sol";
/*
███████╗ █████╗ ██████╗ ██╗ ██╗███████╗██████╗ ██╗ ██╗██████╗
██╔════╝██╔══██╗██╔══██╗██║ ██║██╔════╝██╔══██╗ ██║ ██║╚════██╗
███████╗███████║██████╔╝██║ ██║█████╗ ██████╔╝ ██║ ██║ █████╔╝
╚════██║██╔══██║██╔══██╗██║ ██║██╔══╝ ██╔══██╗ ╚██╗ ██╔╝██╔═══╝
███████║██║ ██║██████╔╝███████╗██║███████╗██║ ██║ ╚████╔╝ ███████╗
╚══════╝╚═╝ ╚═╝╚═════╝ ╚══════╝╚═╝╚══════╝╚═╝ ╚═╝ ╚═══╝ ╚══════╝
███╗ ██╗███████╗████████╗ ██████╗ ███████╗███████╗ ██████╗██████╗ ██╗██████╗ ████████╗ ██████╗ ██████╗
████╗ ██║██╔════╝╚══██╔══╝ ██╔══██╗██╔════╝██╔════╝██╔════╝██╔══██╗██║██╔══██╗╚══██╔══╝██╔═══██╗██╔══██╗
██╔██╗ ██║█████╗ ██║ ██║ ██║█████╗ ███████╗██║ ██████╔╝██║██████╔╝ ██║ ██║ ██║██████╔╝
██║╚██╗██║██╔══╝ ██║ ██║ ██║██╔══╝ ╚════██║██║ ██╔══██╗██║██╔═══╝ ██║ ██║ ██║██╔══██╗
██║ ╚████║██║ ██║ ██████╔╝███████╗███████║╚██████╗██║ ██║██║██║ ██║ ╚██████╔╝██║ ██║
╚═╝ ╚═══╝╚═╝ ╚═╝ ╚═════╝ ╚══════╝╚══════╝ ╚═════╝╚═╝ ╚═╝╚═╝╚═╝ ╚═╝ ╚═════╝ ╚═╝ ╚═╝
*/
/// @title SablierV2NFTDescriptor
/// @notice See the documentation in {ISablierV2NFTDescriptor}.
contract SablierV2NFTDescriptor is ISablierV2NFTDescriptor {
using Strings for address;
using Strings for string;
using Strings for uint256;
/*//////////////////////////////////////////////////////////////////////////
USER-FACING CONSTANT FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @dev Needed to avoid Stack Too Deep.
struct TokenURIVars {
address asset;
string assetSymbol;
uint128 depositedAmount;
bool isTransferable;
string json;
bytes returnData;
ISablierV2Lockup sablier;
string sablierModel;
string sablierStringified;
string status;
string svg;
uint256 streamedPercentage;
bool success;
}
/// @inheritdoc ISablierV2NFTDescriptor
function tokenURI(IERC721Metadata sablier, uint256 streamId) external view override returns (string memory uri) {
TokenURIVars memory vars;
// Load the contracts.
vars.sablier = ISablierV2Lockup(address(sablier));
vars.sablierModel = mapSymbol(sablier);
vars.sablierStringified = address(sablier).toHexString();
vars.asset = address(vars.sablier.getAsset(streamId));
vars.assetSymbol = safeAssetSymbol(vars.asset);
vars.depositedAmount = vars.sablier.getDepositedAmount(streamId);
// Load the stream's data.
vars.status = stringifyStatus(vars.sablier.statusOf(streamId));
vars.streamedPercentage = calculateStreamedPercentage({
streamedAmount: vars.sablier.streamedAmountOf(streamId),
depositedAmount: vars.depositedAmount
});
// Generate the SVG.
vars.svg = NFTSVG.generateSVG(
NFTSVG.SVGParams({
accentColor: generateAccentColor(address(sablier), streamId),
amount: abbreviateAmount({ amount: vars.depositedAmount, decimals: safeAssetDecimals(vars.asset) }),
assetAddress: vars.asset.toHexString(),
assetSymbol: vars.assetSymbol,
duration: calculateDurationInDays({
startTime: vars.sablier.getStartTime(streamId),
endTime: vars.sablier.getEndTime(streamId)
}),
sablierAddress: vars.sablierStringified,
progress: stringifyPercentage(vars.streamedPercentage),
progressNumerical: vars.streamedPercentage,
status: vars.status,
sablierModel: vars.sablierModel
})
);
// Performs a low-level call to handle older deployments that miss the `isTransferable` function.
(vars.success, vars.returnData) =
address(vars.sablier).staticcall(abi.encodeCall(ISablierV2Lockup.isTransferable, (streamId)));
// When the call has failed, the stream NFT is assumed to be transferable.
vars.isTransferable = vars.success ? abi.decode(vars.returnData, (bool)) : true;
// Generate the JSON metadata.
vars.json = string.concat(
'{"attributes":',
generateAttributes({
assetSymbol: vars.assetSymbol,
sender: vars.sablier.getSender(streamId).toHexString(),
status: vars.status
}),
',"description":"',
generateDescription({
sablierModel: vars.sablierModel,
assetSymbol: vars.assetSymbol,
sablierStringified: vars.sablierStringified,
assetAddress: vars.asset.toHexString(),
streamId: streamId.toString(),
isTransferable: vars.isTransferable
}),
'","external_url":"https://sablier.com","name":"',
generateName({ sablierModel: vars.sablierModel, streamId: streamId.toString() }),
'","image":"data:image/svg+xml;base64,',
Base64.encode(bytes(vars.svg)),
'"}'
);
// Encode the JSON metadata in Base64.
uri = string.concat("data:application/json;base64,", Base64.encode(bytes(vars.json)));
}
/*//////////////////////////////////////////////////////////////////////////
INTERNAL CONSTANT FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Creates an abbreviated representation of the provided amount, rounded down and prefixed with ">= ".
/// @dev The abbreviation uses these suffixes:
/// - "K" for thousands
/// - "M" for millions
/// - "B" for billions
/// - "T" for trillions
/// For example, if the input is 1,234,567, the output is ">= 1.23M".
/// @param amount The amount to abbreviate, denoted in units of `decimals`.
/// @param decimals The number of decimals to assume when abbreviating the amount.
/// @return abbreviation The abbreviated representation of the provided amount, as a string.
function abbreviateAmount(uint256 amount, uint256 decimals) internal pure returns (string memory) {
if (amount == 0) {
return "0";
}
uint256 truncatedAmount;
unchecked {
truncatedAmount = decimals == 0 ? amount : amount / 10 ** decimals;
}
// Return dummy values when the truncated amount is either very small or very big.
if (truncatedAmount < 1) {
return string.concat(SVGElements.SIGN_LT, " 1");
} else if (truncatedAmount >= 1e15) {
return string.concat(SVGElements.SIGN_GT, " 999.99T");
}
string[5] memory suffixes = ["", "K", "M", "B", "T"];
uint256 fractionalAmount;
uint256 suffixIndex = 0;
// Truncate repeatedly until the amount is less than 1000.
unchecked {
while (truncatedAmount >= 1000) {
fractionalAmount = (truncatedAmount / 10) % 100; // keep the first two digits after the decimal point
truncatedAmount /= 1000;
suffixIndex += 1;
}
}
// Concatenate the calculated parts to form the final string.
string memory prefix = string.concat(SVGElements.SIGN_GE, " ");
string memory wholePart = truncatedAmount.toString();
string memory fractionalPart = stringifyFractionalAmount(fractionalAmount);
return string.concat(prefix, wholePart, fractionalPart, suffixes[suffixIndex]);
}
/// @notice Calculates the stream's duration in days, rounding down.
function calculateDurationInDays(uint256 startTime, uint256 endTime) internal pure returns (string memory) {
uint256 durationInDays;
unchecked {
durationInDays = (endTime - startTime) / 1 days;
}
// Return dummy values when the duration is either very small or very big.
if (durationInDays == 0) {
return string.concat(SVGElements.SIGN_LT, " 1 Day");
} else if (durationInDays > 9999) {
return string.concat(SVGElements.SIGN_GT, " 9999 Days");
}
string memory suffix = durationInDays == 1 ? " Day" : " Days";
return string.concat(durationInDays.toString(), suffix);
}
/// @notice Calculates how much of the deposited amount has been streamed so far, as a percentage with 4 implied
/// decimals.
function calculateStreamedPercentage(
uint128 streamedAmount,
uint128 depositedAmount
)
internal
pure
returns (uint256)
{
// This cannot overflow because both inputs are uint128s, and zero deposit amounts are not allowed in Sablier.
unchecked {
return streamedAmount * 10_000 / depositedAmount;
}
}
/// @notice Generates a pseudo-random HSL color by hashing together the `chainid`, the `sablier` address,
/// and the `streamId`. This will be used as the accent color for the SVG.
function generateAccentColor(address sablier, uint256 streamId) internal view returns (string memory) {
// The chain ID is part of the hash so that the generated color is different across chains.
uint256 chainId = block.chainid;
// Hash the parameters to generate a pseudo-random bit field, which will be used as entropy.
// | Hue | Saturation | Lightness | -> Roles
// | [31:16] | [15:8] | [7:0] | -> Bit positions
uint32 bitField = uint32(uint256(keccak256(abi.encodePacked(chainId, sablier, streamId))));
unchecked {
// The hue is a degree on a color wheel, so its range is [0, 360).
// Shifting 16 bits to the right means using the bits at positions [31:16].
uint256 hue = (bitField >> 16) % 360;
// The saturation is a percentage where 0% is grayscale and 100%, but here the range is bounded to [20,100]
// to make the colors more lively.
// Shifting 8 bits to the right and applying an 8-bit mask means using the bits at positions [15:8].
uint256 saturation = ((bitField >> 8) & 0xFF) % 80 + 20;
// The lightness is typically a percentage between 0% (black) and 100% (white), but here the range
// is bounded to [30,100] to avoid dark colors.
// Applying an 8-bit mask means using the bits at positions [7:0].
uint256 lightness = (bitField & 0xFF) % 70 + 30;
// Finally, concatenate the HSL values to form an SVG color string.
return string.concat("hsl(", hue.toString(), ",", saturation.toString(), "%,", lightness.toString(), "%)");
}
}
/// @notice Generates an array of JSON objects that represent the NFT's attributes:
/// - Asset symbol
/// - Sender address
/// - Status
/// @dev These attributes are useful for filtering and sorting the NFTs.
function generateAttributes(
string memory assetSymbol,
string memory sender,
string memory status
)
internal
pure
returns (string memory)
{
return string.concat(
'[{"trait_type":"Asset","value":"',
assetSymbol,
'"},{"trait_type":"Sender","value":"',
sender,
'"},{"trait_type":"Status","value":"',
status,
'"}]'
);
}
/// @notice Generates a string with the NFT's JSON metadata description, which provides a high-level overview.
function generateDescription(
string memory sablierModel,
string memory assetSymbol,
string memory sablierStringified,
string memory assetAddress,
string memory streamId,
bool isTransferable
)
internal
pure
returns (string memory)
{
// Depending on the transferability of the NFT, declare the relevant information.
string memory info = isTransferable
?
unicode"⚠️ WARNING: Transferring the NFT makes the new owner the recipient of the stream. The funds are not automatically withdrawn for the previous recipient."
: unicode"❕INFO: This NFT is non-transferable. It cannot be sold or transferred to another account.";
return string.concat(
"This NFT represents a payment stream in a Sablier V2 ",
sablierModel,
" contract. The owner of this NFT can withdraw the streamed assets, which are denominated in ",
assetSymbol,
".\\n\\n- Stream ID: ",
streamId,
"\\n- ",
sablierModel,
" Address: ",
sablierStringified,
"\\n- ",
assetSymbol,
" Address: ",
assetAddress,
"\\n\\n",
info
);
}
/// @notice Generates a string with the NFT's JSON metadata name, which is unique for each stream.
/// @dev The `streamId` is equivalent to the ERC-721 `tokenId`.
function generateName(string memory sablierModel, string memory streamId) internal pure returns (string memory) {
return string.concat("Sablier V2 ", sablierModel, " #", streamId);
}
/// @notice Checks whether the provided string contains only alphanumeric characters, spaces, and dashes.
/// @dev Note that this returns true for empty strings.
function isAllowedCharacter(string memory str) internal pure returns (bool) {
// Convert the string to bytes to iterate over its characters.
bytes memory b = bytes(str);
uint256 length = b.length;
for (uint256 i = 0; i < length; ++i) {
bytes1 char = b[i];
// Check if it's a space, dash, or an alphanumeric character.
bool isSpace = char == 0x20; // space
bool isDash = char == 0x2D; // dash
bool isDigit = char >= 0x30 && char <= 0x39; // 0-9
bool isUppercaseLetter = char >= 0x41 && char <= 0x5A; // A-Z
bool isLowercaseLetter = char >= 0x61 && char <= 0x7A; // a-z
if (!(isSpace || isDash || isDigit || isUppercaseLetter || isLowercaseLetter)) {
return false;
}
}
return true;
}
/// @notice Maps ERC-721 symbols to human-readable model names.
/// @dev Reverts if the symbol is unknown.
function mapSymbol(IERC721Metadata sablier) internal view returns (string memory) {
string memory symbol = sablier.symbol();
if (symbol.equal("SAB-V2-LOCKUP-LIN")) {
return "Lockup Linear";
} else if (symbol.equal("SAB-V2-LOCKUP-DYN")) {
return "Lockup Dynamic";
} else if (symbol.equal("SAB-V2-LOCKUP-TRA")) {
return "Lockup Tranched";
} else {
revert Errors.SablierV2NFTDescriptor_UnknownNFT(sablier, symbol);
}
}
/// @notice Retrieves the asset's decimals safely, defaulting to "0" if an error occurs.
/// @dev Performs a low-level call to handle assets in which the decimals are not implemented.
function safeAssetDecimals(address asset) internal view returns (uint8) {
(bool success, bytes memory returnData) = asset.staticcall(abi.encodeCall(IERC20Metadata.decimals, ()));
if (success && returnData.length == 32) {
return abi.decode(returnData, (uint8));
} else {
return 0;
}
}
/// @notice Retrieves the asset's symbol safely, defaulting to a hard-coded value if an error occurs.
/// @dev Performs a low-level call to handle assets in which the symbol is not implemented or it is a bytes32
/// instead of a string.
function safeAssetSymbol(address asset) internal view returns (string memory) {
(bool success, bytes memory returnData) = asset.staticcall(abi.encodeCall(IERC20Metadata.symbol, ()));
// Non-empty strings have a length greater than 64, and bytes32 has length 32.
if (!success || returnData.length <= 64) {
return "ERC20";
}
string memory symbol = abi.decode(returnData, (string));
// Check if the symbol is too long or contains disallowed characters. This measure helps mitigate potential
// security threats from malicious assets injecting scripts in the symbol string.
if (bytes(symbol).length > 30) {
return "Long Symbol";
} else {
if (!isAllowedCharacter(symbol)) {
return "Unsupported Symbol";
}
return symbol;
}
}
/// @notice Converts the provided fractional amount to a string prefixed by a dot.
/// @param fractionalAmount A numerical value with 2 implied decimals.
function stringifyFractionalAmount(uint256 fractionalAmount) internal pure returns (string memory) {
// Return the empty string if the fractional amount is zero.
if (fractionalAmount == 0) {
return "";
}
// Add a leading zero if the fractional part is less than 10, e.g. for "1", this function returns ".01%".
else if (fractionalAmount < 10) {
return string.concat(".0", fractionalAmount.toString());
}
// Otherwise, stringify the fractional amount simply.
else {
return string.concat(".", fractionalAmount.toString());
}
}
/// @notice Converts the provided percentage to a string.
/// @param percentage A numerical value with 4 implied decimals.
function stringifyPercentage(uint256 percentage) internal pure returns (string memory) {
// Extract the last two decimals.
string memory fractionalPart = stringifyFractionalAmount(percentage % 100);
// Remove the last two decimals.
string memory wholePart = (percentage / 100).toString();
// Concatenate the whole and fractional parts.
return string.concat(wholePart, fractionalPart, "%");
}
/// @notice Retrieves the stream's status as a string.
function stringifyStatus(Lockup.Status status) internal pure returns (string memory) {
if (status == Lockup.Status.DEPLETED) {
return "Depleted";
} else if (status == Lockup.Status.CANCELED) {
return "Canceled";
} else if (status == Lockup.Status.STREAMING) {
return "Streaming";
} else if (status == Lockup.Status.SETTLED) {
return "Settled";
} else {
return "Pending";
}
}
}// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;
import { IERC721Metadata } from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
import { UD60x18 } from "@prb/math/src/UD60x18.sol";
/// @title Errors
/// @notice Library containing all custom errors the protocol may revert with.
library Errors {
/*//////////////////////////////////////////////////////////////////////////
GENERICS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Thrown when `msg.sender` is not the admin.
error CallerNotAdmin(address admin, address caller);
/// @notice Thrown when trying to delegate call to a function that disallows delegate calls.
error DelegateCall();
/*//////////////////////////////////////////////////////////////////////////
SABLIER-V2-LOCKUP
//////////////////////////////////////////////////////////////////////////*/
/// @notice Thrown when trying to allow to hook a contract that doesn't implement the interface correctly.
error SablierV2Lockup_AllowToHookUnsupportedInterface(address recipient);
/// @notice Thrown when trying to allow to hook an address with no code.
error SablierV2Lockup_AllowToHookZeroCodeSize(address recipient);
/// @notice Thrown when the broker fee exceeds the maximum allowed fee.
error SablierV2Lockup_BrokerFeeTooHigh(UD60x18 brokerFee, UD60x18 maxBrokerFee);
/// @notice Thrown when trying to create a stream with a zero deposit amount.
error SablierV2Lockup_DepositAmountZero();
/// @notice Thrown when trying to create a stream with an end time not in the future.
error SablierV2Lockup_EndTimeNotInTheFuture(uint40 blockTimestamp, uint40 endTime);
/// @notice Thrown when the hook does not return the correct selector.
error SablierV2Lockup_InvalidHookSelector(address recipient);
/// @notice Thrown when trying to transfer Stream NFT when transferability is disabled.
error SablierV2Lockup_NotTransferable(uint256 tokenId);
/// @notice Thrown when the ID references a null stream.
error SablierV2Lockup_Null(uint256 streamId);
/// @notice Thrown when trying to withdraw an amount greater than the withdrawable amount.
error SablierV2Lockup_Overdraw(uint256 streamId, uint128 amount, uint128 withdrawableAmount);
/// @notice Thrown when trying to create a stream with a zero start time.
error SablierV2Lockup_StartTimeZero();
/// @notice Thrown when trying to cancel or renounce a canceled stream.
error SablierV2Lockup_StreamCanceled(uint256 streamId);
/// @notice Thrown when trying to cancel, renounce, or withdraw from a depleted stream.
error SablierV2Lockup_StreamDepleted(uint256 streamId);
/// @notice Thrown when trying to cancel or renounce a stream that is not cancelable.
error SablierV2Lockup_StreamNotCancelable(uint256 streamId);
/// @notice Thrown when trying to burn a stream that is not depleted.
error SablierV2Lockup_StreamNotDepleted(uint256 streamId);
/// @notice Thrown when trying to cancel or renounce a settled stream.
error SablierV2Lockup_StreamSettled(uint256 streamId);
/// @notice Thrown when `msg.sender` lacks authorization to perform an action.
error SablierV2Lockup_Unauthorized(uint256 streamId, address caller);
/// @notice Thrown when trying to withdraw to an address other than the recipient's.
error SablierV2Lockup_WithdrawalAddressNotRecipient(uint256 streamId, address caller, address to);
/// @notice Thrown when trying to withdraw zero assets from a stream.
error SablierV2Lockup_WithdrawAmountZero(uint256 streamId);
/// @notice Thrown when trying to withdraw from multiple streams and the number of stream IDs does
/// not match the number of withdraw amounts.
error SablierV2Lockup_WithdrawArrayCountsNotEqual(uint256 streamIdsCount, uint256 amountsCount);
/// @notice Thrown when trying to withdraw to the zero address.
error SablierV2Lockup_WithdrawToZeroAddress(uint256 streamId);
/*//////////////////////////////////////////////////////////////////////////
SABLIER-V2-LOCKUP-DYNAMIC
//////////////////////////////////////////////////////////////////////////*/
/// @notice Thrown when trying to create a stream with a deposit amount not equal to the sum of the
/// segment amounts.
error SablierV2LockupDynamic_DepositAmountNotEqualToSegmentAmountsSum(
uint128 depositAmount, uint128 segmentAmountsSum
);
/// @notice Thrown when trying to create a stream with more segments than the maximum allowed.
error SablierV2LockupDynamic_SegmentCountTooHigh(uint256 count);
/// @notice Thrown when trying to create a stream with no segments.
error SablierV2LockupDynamic_SegmentCountZero();
/// @notice Thrown when trying to create a stream with unordered segment timestamps.
error SablierV2LockupDynamic_SegmentTimestampsNotOrdered(
uint256 index, uint40 previousTimestamp, uint40 currentTimestamp
);
/// @notice Thrown when trying to create a stream with a start time not strictly less than the first
/// segment timestamp.
error SablierV2LockupDynamic_StartTimeNotLessThanFirstSegmentTimestamp(
uint40 startTime, uint40 firstSegmentTimestamp
);
/*//////////////////////////////////////////////////////////////////////////
SABLIER-V2-LOCKUP-LINEAR
//////////////////////////////////////////////////////////////////////////*/
/// @notice Thrown when trying to create a stream with a cliff time not strictly less than the end time.
error SablierV2LockupLinear_CliffTimeNotLessThanEndTime(uint40 cliffTime, uint40 endTime);
/// @notice Thrown when trying to create a stream with a start time not strictly less than the cliff time, when the
/// cliff time does not have a zero value.
error SablierV2LockupLinear_StartTimeNotLessThanCliffTime(uint40 startTime, uint40 cliffTime);
/// @notice Thrown when trying to create a stream with a start time not strictly less than the end time.
error SablierV2LockupLinear_StartTimeNotLessThanEndTime(uint40 startTime, uint40 endTime);
/*//////////////////////////////////////////////////////////////////////////
SABLIER-V2-NFT-DESCRIPTOR
//////////////////////////////////////////////////////////////////////////*/
/// @notice Thrown when trying to generate the token URI for an unknown ERC-721 NFT contract.
error SablierV2NFTDescriptor_UnknownNFT(IERC721Metadata nft, string symbol);
/*//////////////////////////////////////////////////////////////////////////
SABLIER-V2-LOCKUP-TRANCHE
//////////////////////////////////////////////////////////////////////////*/
/// @notice Thrown when trying to create a stream with a deposit amount not equal to the sum of the
/// tranche amounts.
error SablierV2LockupTranched_DepositAmountNotEqualToTrancheAmountsSum(
uint128 depositAmount, uint128 trancheAmountsSum
);
/// @notice Thrown when trying to create a stream with a start time not strictly less than the first
/// tranche timestamp.
error SablierV2LockupTranched_StartTimeNotLessThanFirstTrancheTimestamp(
uint40 startTime, uint40 firstTrancheTimestamp
);
/// @notice Thrown when trying to create a stream with more tranches than the maximum allowed.
error SablierV2LockupTranched_TrancheCountTooHigh(uint256 count);
/// @notice Thrown when trying to create a stream with no tranches.
error SablierV2LockupTranched_TrancheCountZero();
/// @notice Thrown when trying to create a stream with unordered tranche timestamps.
error SablierV2LockupTranched_TrancheTimestampsNotOrdered(
uint256 index, uint40 previousTimestamp, uint40 currentTimestamp
);
}// SPDX-License-Identifier: GPL-3.0-or-later
// solhint-disable quotes
pragma solidity >=0.8.22;
import { Strings } from "@openzeppelin/contracts/utils/Strings.sol";
import { SVGElements } from "./SVGElements.sol";
library NFTSVG {
using Strings for uint256;
uint256 internal constant CARD_MARGIN = 16;
struct SVGParams {
string accentColor;
string amount;
string assetAddress;
string assetSymbol;
string duration;
string progress;
uint256 progressNumerical;
string sablierAddress;
string sablierModel;
string status;
}
struct SVGVars {
string amountCard;
uint256 amountWidth;
uint256 amountXPosition;
string cards;
uint256 cardsWidth;
string durationCard;
uint256 durationWidth;
uint256 durationXPosition;
string progressCard;
uint256 progressWidth;
uint256 progressXPosition;
string statusCard;
uint256 statusWidth;
uint256 statusXPosition;
}
function generateSVG(SVGParams memory params) internal pure returns (string memory) {
SVGVars memory vars;
// Generate the progress card.
(vars.progressWidth, vars.progressCard) = SVGElements.card({
cardType: SVGElements.CardType.PROGRESS,
content: params.progress,
circle: SVGElements.progressCircle({
progressNumerical: params.progressNumerical,
accentColor: params.accentColor
})
});
// Generate the status card.
(vars.statusWidth, vars.statusCard) =
SVGElements.card({ cardType: SVGElements.CardType.STATUS, content: params.status });
// Generate the deposit amount card.
(vars.amountWidth, vars.amountCard) =
SVGElements.card({ cardType: SVGElements.CardType.AMOUNT, content: params.amount });
// Generate the duration card.
(vars.durationWidth, vars.durationCard) =
SVGElements.card({ cardType: SVGElements.CardType.DURATION, content: params.duration });
unchecked {
// Calculate the width of the row containing the cards and the margins between them.
vars.cardsWidth =
vars.amountWidth + vars.durationWidth + vars.progressWidth + vars.statusWidth + CARD_MARGIN * 3;
// Calculate the positions on the X axis based on the following layout:
//
// ___________________________ SVG Width (1000px) ___________________________
// | | | | | | | | | |
// | <-> | Progress | 16px | Status | 16px | Amount | 16px | Duration | <-> |
vars.progressXPosition = (1000 - vars.cardsWidth) / 2;
vars.statusXPosition = vars.progressXPosition + vars.progressWidth + CARD_MARGIN;
vars.amountXPosition = vars.statusXPosition + vars.statusWidth + CARD_MARGIN;
vars.durationXPosition = vars.amountXPosition + vars.amountWidth + CARD_MARGIN;
}
// Concatenate all cards.
vars.cards = string.concat(vars.progressCard, vars.statusCard, vars.amountCard, vars.durationCard);
return string.concat(
'<svg xmlns="http://www.w3.org/2000/svg" width="1000" height="1000" viewBox="0 0 1000 1000">',
SVGElements.BACKGROUND,
generateDefs(params.accentColor, params.status, vars.cards),
generateFloatingText(params.sablierAddress, params.sablierModel, params.assetAddress, params.assetSymbol),
generateHrefs(vars.progressXPosition, vars.statusXPosition, vars.amountXPosition, vars.durationXPosition),
"</svg>"
);
}
function generateDefs(
string memory accentColor,
string memory status,
string memory cards
)
internal
pure
returns (string memory)
{
return string.concat(
"<defs>",
SVGElements.GLOW,
SVGElements.NOISE,
SVGElements.LOGO,
SVGElements.FLOATING_TEXT,
SVGElements.gradients(accentColor),
SVGElements.hourglass(status),
cards,
"</defs>"
);
}
function generateFloatingText(
string memory sablierAddress,
string memory sablierModel,
string memory assetAddress,
string memory assetSymbol
)
internal
pure
returns (string memory)
{
return string.concat(
'<text text-rendering="optimizeSpeed">',
SVGElements.floatingText({
offset: "-100%",
text: string.concat(sablierAddress, unicode" • ", "Sablier V2 ", sablierModel)
}),
SVGElements.floatingText({
offset: "0%",
text: string.concat(sablierAddress, unicode" • ", "Sablier V2 ", sablierModel)
}),
SVGElements.floatingText({ offset: "-50%", text: string.concat(assetAddress, unicode" • ", assetSymbol) }),
SVGElements.floatingText({ offset: "50%", text: string.concat(assetAddress, unicode" • ", assetSymbol) }),
"</text>"
);
}
function generateHrefs(
uint256 progressXPosition,
uint256 statusXPosition,
uint256 amountXPosition,
uint256 durationXPosition
)
internal
pure
returns (string memory)
{
return string.concat(
'<use href="#Glow" fill-opacity=".9"/>',
'<use href="#Glow" x="1000" y="1000" fill-opacity=".9"/>',
'<use href="#Logo" x="170" y="170" transform="scale(.6)"/>'
'<use href="#Hourglass" x="150" y="90" transform="rotate(10)" transform-origin="500 500"/>',
'<use href="#Progress" x="',
progressXPosition.toString(),
'" y="790"/>',
'<use href="#Status" x="',
statusXPosition.toString(),
'" y="790"/>',
'<use href="#Amount" x="',
amountXPosition.toString(),
'" y="790"/>',
'<use href="#Duration" x="',
durationXPosition.toString(),
'" y="790"/>'
);
}
}// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;
import { IERC4906 } from "@openzeppelin/contracts/interfaces/IERC4906.sol";
import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { IERC721Metadata } from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
import { UD60x18 } from "@prb/math/src/UD60x18.sol";
import { Lockup } from "../types/DataTypes.sol";
import { IAdminable } from "./IAdminable.sol";
import { ISablierV2NFTDescriptor } from "./ISablierV2NFTDescriptor.sol";
/// @title ISablierV2Lockup
/// @notice Common logic between all Sablier V2 Lockup contracts.
interface ISablierV2Lockup is
IAdminable, // 0 inherited components
IERC4906, // 2 inherited components
IERC721Metadata // 2 inherited components
{
/*//////////////////////////////////////////////////////////////////////////
EVENTS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Emitted when the admin allows a new recipient contract to hook to Sablier.
/// @param admin The address of the current contract admin.
/// @param recipient The address of the recipient contract put on the allowlist.
event AllowToHook(address indexed admin, address recipient);
/// @notice Emitted when a stream is canceled.
/// @param streamId The ID of the stream.
/// @param sender The address of the stream's sender.
/// @param recipient The address of the stream's recipient.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param senderAmount The amount of assets refunded to the stream's sender, denoted in units of the asset's
/// decimals.
/// @param recipientAmount The amount of assets left for the stream's recipient to withdraw, denoted in units of the
/// asset's decimals.
event CancelLockupStream(
uint256 streamId,
address indexed sender,
address indexed recipient,
IERC20 indexed asset,
uint128 senderAmount,
uint128 recipientAmount
);
/// @notice Emitted when a sender gives up the right to cancel a stream.
/// @param streamId The ID of the stream.
event RenounceLockupStream(uint256 indexed streamId);
/// @notice Emitted when the admin sets a new NFT descriptor contract.
/// @param admin The address of the current contract admin.
/// @param oldNFTDescriptor The address of the old NFT descriptor contract.
/// @param newNFTDescriptor The address of the new NFT descriptor contract.
event SetNFTDescriptor(
address indexed admin, ISablierV2NFTDescriptor oldNFTDescriptor, ISablierV2NFTDescriptor newNFTDescriptor
);
/// @notice Emitted when assets are withdrawn from a stream.
/// @param streamId The ID of the stream.
/// @param to The address that has received the withdrawn assets.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param amount The amount of assets withdrawn, denoted in units of the asset's decimals.
event WithdrawFromLockupStream(uint256 indexed streamId, address indexed to, IERC20 indexed asset, uint128 amount);
/*//////////////////////////////////////////////////////////////////////////
CONSTANT FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Retrieves the address of the ERC-20 asset to be distributed.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function getAsset(uint256 streamId) external view returns (IERC20 asset);
/// @notice Retrieves the amount deposited in the stream, denoted in units of the asset's decimals.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function getDepositedAmount(uint256 streamId) external view returns (uint128 depositedAmount);
/// @notice Retrieves the stream's end time, which is a Unix timestamp.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function getEndTime(uint256 streamId) external view returns (uint40 endTime);
/// @notice Retrieves the stream's recipient.
/// @dev Reverts if the NFT has been burned.
/// @param streamId The stream ID for the query.
function getRecipient(uint256 streamId) external view returns (address recipient);
/// @notice Retrieves the amount refunded to the sender after a cancellation, denoted in units of the asset's
/// decimals. This amount is always zero unless the stream was canceled.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function getRefundedAmount(uint256 streamId) external view returns (uint128 refundedAmount);
/// @notice Retrieves the stream's sender.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function getSender(uint256 streamId) external view returns (address sender);
/// @notice Retrieves the stream's start time, which is a Unix timestamp.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function getStartTime(uint256 streamId) external view returns (uint40 startTime);
/// @notice Retrieves the amount withdrawn from the stream, denoted in units of the asset's decimals.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function getWithdrawnAmount(uint256 streamId) external view returns (uint128 withdrawnAmount);
/// @notice Retrieves a flag indicating whether the provided address is a contract allowed to hook to Sablier
/// when a stream is canceled or when assets are withdrawn.
/// @dev See {ISablierLockupRecipient} for more information.
function isAllowedToHook(address recipient) external view returns (bool result);
/// @notice Retrieves a flag indicating whether the stream can be canceled. When the stream is cold, this
/// flag is always `false`.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function isCancelable(uint256 streamId) external view returns (bool result);
/// @notice Retrieves a flag indicating whether the stream is cold, i.e. settled, canceled, or depleted.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function isCold(uint256 streamId) external view returns (bool result);
/// @notice Retrieves a flag indicating whether the stream is depleted.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function isDepleted(uint256 streamId) external view returns (bool result);
/// @notice Retrieves a flag indicating whether the stream exists.
/// @dev Does not revert if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function isStream(uint256 streamId) external view returns (bool result);
/// @notice Retrieves a flag indicating whether the stream NFT can be transferred.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function isTransferable(uint256 streamId) external view returns (bool result);
/// @notice Retrieves a flag indicating whether the stream is warm, i.e. either pending or streaming.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function isWarm(uint256 streamId) external view returns (bool result);
/// @notice Retrieves the maximum broker fee that can be charged by the broker, denoted as a fixed-point
/// number where 1e18 is 100%.
/// @dev This value is hard coded as a constant.
function MAX_BROKER_FEE() external view returns (UD60x18);
/// @notice Counter for stream IDs, used in the create functions.
function nextStreamId() external view returns (uint256);
/// @notice Contract that generates the non-fungible token URI.
function nftDescriptor() external view returns (ISablierV2NFTDescriptor);
/// @notice Calculates the amount that the sender would be refunded if the stream were canceled, denoted in units
/// of the asset's decimals.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function refundableAmountOf(uint256 streamId) external view returns (uint128 refundableAmount);
/// @notice Retrieves the stream's status.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function statusOf(uint256 streamId) external view returns (Lockup.Status status);
/// @notice Calculates the amount streamed to the recipient, denoted in units of the asset's decimals.
/// @dev Reverts if `streamId` references a null stream.
///
/// Notes:
/// - Upon cancellation of the stream, the amount streamed is calculated as the difference between the deposited
/// amount and the refunded amount. Ultimately, when the stream becomes depleted, the streamed amount is equivalent
/// to the total amount withdrawn.
///
/// @param streamId The stream ID for the query.
function streamedAmountOf(uint256 streamId) external view returns (uint128 streamedAmount);
/// @notice Retrieves a flag indicating whether the stream was canceled.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function wasCanceled(uint256 streamId) external view returns (bool result);
/// @notice Calculates the amount that the recipient can withdraw from the stream, denoted in units of the asset's
/// decimals.
/// @dev Reverts if `streamId` references a null stream.
/// @param streamId The stream ID for the query.
function withdrawableAmountOf(uint256 streamId) external view returns (uint128 withdrawableAmount);
/*//////////////////////////////////////////////////////////////////////////
NON-CONSTANT FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Allows a recipient contract to hook to Sablier when a stream is canceled or when assets are withdrawn.
/// Useful for implementing contracts that hold streams on behalf of users, such as vaults or staking contracts.
///
/// @dev Emits an {AllowToHook} event.
///
/// Notes:
/// - Does not revert if the contract is already on the allowlist.
/// - This is an irreversible operation. The contract cannot be removed from the allowlist.
///
/// Requirements:
/// - `msg.sender` must be the contract admin.
/// - `recipient` must have a non-zero code size.
/// - `recipient` must implement {ISablierLockupRecipient}.
///
/// @param recipient The address of the contract to allow for hooks.
function allowToHook(address recipient) external;
/// @notice Burns the NFT associated with the stream.
///
/// @dev Emits a {Transfer} event.
///
/// Requirements:
/// - Must not be delegate called.
/// - `streamId` must reference a depleted stream.
/// - The NFT must exist.
/// - `msg.sender` must be either the NFT owner or an approved third party.
///
/// @param streamId The ID of the stream NFT to burn.
function burn(uint256 streamId) external;
/// @notice Cancels the stream and refunds any remaining assets to the sender.
///
/// @dev Emits a {Transfer}, {CancelLockupStream}, and {MetadataUpdate} event.
///
/// Notes:
/// - If there any assets left for the recipient to withdraw, the stream is marked as canceled. Otherwise, the
/// stream is marked as depleted.
/// - This function attempts to invoke a hook on the recipient, if the resolved address is a contract.
///
/// Requirements:
/// - Must not be delegate called.
/// - The stream must be warm and cancelable.
/// - `msg.sender` must be the stream's sender.
///
/// @param streamId The ID of the stream to cancel.
function cancel(uint256 streamId) external;
/// @notice Cancels multiple streams and refunds any remaining assets to the sender.
///
/// @dev Emits multiple {Transfer}, {CancelLockupStream}, and {MetadataUpdate} events.
///
/// Notes:
/// - Refer to the notes in {cancel}.
///
/// Requirements:
/// - All requirements from {cancel} must be met for each stream.
///
/// @param streamIds The IDs of the streams to cancel.
function cancelMultiple(uint256[] calldata streamIds) external;
/// @notice Removes the right of the stream's sender to cancel the stream.
///
/// @dev Emits a {RenounceLockupStream} and {MetadataUpdate} event.
///
/// Notes:
/// - This is an irreversible operation.
///
/// Requirements:
/// - Must not be delegate called.
/// - `streamId` must reference a warm stream.
/// - `msg.sender` must be the stream's sender.
/// - The stream must be cancelable.
///
/// @param streamId The ID of the stream to renounce.
function renounce(uint256 streamId) external;
/// @notice Sets a new NFT descriptor contract, which produces the URI describing the Sablier stream NFTs.
///
/// @dev Emits a {SetNFTDescriptor} and {BatchMetadataUpdate} event.
///
/// Notes:
/// - Does not revert if the NFT descriptor is the same.
///
/// Requirements:
/// - `msg.sender` must be the contract admin.
///
/// @param newNFTDescriptor The address of the new NFT descriptor contract.
function setNFTDescriptor(ISablierV2NFTDescriptor newNFTDescriptor) external;
/// @notice Withdraws the provided amount of assets from the stream to the `to` address.
///
/// @dev Emits a {Transfer}, {WithdrawFromLockupStream}, and {MetadataUpdate} event.
///
/// Notes:
/// - This function attempts to call a hook on the recipient of the stream, unless `msg.sender` is the recipient.
///
/// Requirements:
/// - Must not be delegate called.
/// - `streamId` must not reference a null or depleted stream.
/// - `to` must not be the zero address.
/// - `amount` must be greater than zero and must not exceed the withdrawable amount.
/// - `to` must be the recipient if `msg.sender` is not the stream's recipient or an approved third party.
///
/// @param streamId The ID of the stream to withdraw from.
/// @param to The address receiving the withdrawn assets.
/// @param amount The amount to withdraw, denoted in units of the asset's decimals.
function withdraw(uint256 streamId, address to, uint128 amount) external;
/// @notice Withdraws the maximum withdrawable amount from the stream to the provided address `to`.
///
/// @dev Emits a {Transfer}, {WithdrawFromLockupStream}, and {MetadataUpdate} event.
///
/// Notes:
/// - Refer to the notes in {withdraw}.
///
/// Requirements:
/// - Refer to the requirements in {withdraw}.
///
/// @param streamId The ID of the stream to withdraw from.
/// @param to The address receiving the withdrawn assets.
/// @return withdrawnAmount The amount withdrawn, denoted in units of the asset's decimals.
function withdrawMax(uint256 streamId, address to) external returns (uint128 withdrawnAmount);
/// @notice Withdraws the maximum withdrawable amount from the stream to the current recipient, and transfers the
/// NFT to `newRecipient`.
///
/// @dev Emits a {WithdrawFromLockupStream} and a {Transfer} event.
///
/// Notes:
/// - If the withdrawable amount is zero, the withdrawal is skipped.
/// - Refer to the notes in {withdraw}.
///
/// Requirements:
/// - `msg.sender` must be the stream's recipient.
/// - Refer to the requirements in {withdraw}.
/// - Refer to the requirements in {IERC721.transferFrom}.
///
/// @param streamId The ID of the stream NFT to transfer.
/// @param newRecipient The address of the new owner of the stream NFT.
/// @return withdrawnAmount The amount withdrawn, denoted in units of the asset's decimals.
function withdrawMaxAndTransfer(
uint256 streamId,
address newRecipient
)
external
returns (uint128 withdrawnAmount);
/// @notice Withdraws assets from streams to the recipient of each stream.
///
/// @dev Emits multiple {Transfer}, {WithdrawFromLockupStream}, and {MetadataUpdate} events.
///
/// Notes:
/// - This function attempts to call a hook on the recipient of each stream, unless `msg.sender` is the recipient.
///
/// Requirements:
/// - Must not be delegate called.
/// - There must be an equal number of `streamIds` and `amounts`.
/// - Each stream ID in the array must not reference a null or depleted stream.
/// - Each amount in the array must be greater than zero and must not exceed the withdrawable amount.
///
/// @param streamIds The IDs of the streams to withdraw from.
/// @param amounts The amounts to withdraw, denoted in units of the asset's decimals.
function withdrawMultiple(uint256[] calldata streamIds, uint128[] calldata amounts) external;
}// SPDX-License-Identifier: GPL-3.0-or-later
// solhint-disable max-line-length,quotes
pragma solidity >=0.8.22;
import { Math } from "@openzeppelin/contracts/utils/math/Math.sol";
import { Strings } from "@openzeppelin/contracts/utils/Strings.sol";
library SVGElements {
using Strings for string;
using Strings for uint256;
/*//////////////////////////////////////////////////////////////////////////
CONSTANTS
//////////////////////////////////////////////////////////////////////////*/
string internal constant BACKGROUND =
'<rect width="100%" height="100%" filter="url(#Noise)"/><rect x="70" y="70" width="860" height="860" fill="#fff" fill-opacity=".03" rx="45" ry="45" stroke="#fff" stroke-opacity=".1" stroke-width="4"/>';
string internal constant BACKGROUND_COLOR = "hsl(230,21%,11%)";
string internal constant FLOATING_TEXT =
'<path id="FloatingText" fill="none" d="M125 45h750s80 0 80 80v750s0 80 -80 80h-750s-80 0 -80 -80v-750s0 -80 80 -80"/>';
string internal constant GLOW = '<circle id="Glow" r="500" fill="url(#RadialGlow)"/>';
string internal constant LOGO =
'<path id="Logo" fill="#fff" fill-opacity=".1" d="m133.559,124.034c-.013,2.412-1.059,4.848-2.923,6.402-2.558,1.819-5.168,3.439-7.888,4.996-14.44,8.262-31.047,12.565-47.674,12.569-8.858.036-17.838-1.272-26.328-3.663-9.806-2.766-19.087-7.113-27.562-12.778-13.842-8.025,9.468-28.606,16.153-35.265h0c2.035-1.838,4.252-3.546,6.463-5.224h0c6.429-5.655,16.218-2.835,20.358,4.17,4.143,5.057,8.816,9.649,13.92,13.734h.037c5.736,6.461,15.357-2.253,9.38-8.48,0,0-3.515-3.515-3.515-3.515-11.49-11.478-52.656-52.664-64.837-64.837l.049-.037c-1.725-1.606-2.719-3.847-2.751-6.204h0c-.046-2.375,1.062-4.582,2.726-6.229h0l.185-.148h0c.099-.062,.222-.148,.37-.259h0c2.06-1.362,3.951-2.621,6.044-3.842C57.763-3.473,97.76-2.341,128.637,18.332c16.671,9.946-26.344,54.813-38.651,40.199-6.299-6.096-18.063-17.743-19.668-18.811-6.016-4.047-13.061,4.776-7.752,9.751l68.254,68.371c1.724,1.601,2.714,3.84,2.738,6.192Z"/>';
string internal constant HOURGLASS_BACKGROUND_CIRCLE =
'<path d="M 50,360 a 300,300 0 1,1 600,0 a 300,300 0 1,1 -600,0" fill="#fff" fill-opacity=".02" stroke="url(#HourglassStroke)" stroke-width="4"/>';
string internal constant HOURGLASS_FILL =
'<path d="m566,161.201v-53.924c0-19.382-22.513-37.563-63.398-51.198-40.756-13.592-94.946-21.079-152.587-21.079s-111.838,7.487-152.602,21.079c-40.893,13.636-63.413,31.816-63.413,51.198v53.924c0,17.181,17.704,33.427,50.223,46.394v284.809c-32.519,12.96-50.223,29.206-50.223,46.394v53.924c0,19.382,22.52,37.563,63.413,51.198,40.763,13.592,94.954,21.079,152.602,21.079s111.831-7.487,152.587-21.079c40.886-13.636,63.398-31.816,63.398-51.198v-53.924c0-17.196-17.704-33.435-50.223-46.401V207.603c32.519-12.967,50.223-29.206,50.223-46.401Zm-347.462,57.793l130.959,131.027-130.959,131.013V218.994Zm262.924.022v262.018l-130.937-131.006,130.937-131.013Z" fill="#161822"></path>';
string internal constant HOURGLASS_STROKE =
'<g fill="none" stroke="url(#HourglassStroke)" stroke-linecap="round" stroke-miterlimit="10" stroke-width="4"><path d="m565.641,107.28c0,9.537-5.56,18.629-15.676,26.973h-.023c-9.204,7.596-22.194,14.562-38.197,20.592-39.504,14.936-97.325,24.355-161.733,24.355-90.48,0-167.948-18.582-199.953-44.948h-.023c-10.115-8.344-15.676-17.437-15.676-26.973,0-39.735,96.554-71.921,215.652-71.921s215.629,32.185,215.629,71.921Z"/><path d="m134.36,161.203c0,39.735,96.554,71.921,215.652,71.921s215.629-32.186,215.629-71.921"/><line x1="134.36" y1="161.203" x2="134.36" y2="107.28"/><line x1="565.64" y1="161.203" x2="565.64" y2="107.28"/><line x1="184.584" y1="206.823" x2="184.585" y2="537.579"/><line x1="218.181" y1="218.118" x2="218.181" y2="562.537"/><line x1="481.818" y1="218.142" x2="481.819" y2="562.428"/><line x1="515.415" y1="207.352" x2="515.416" y2="537.579"/><path d="m184.58,537.58c0,5.45,4.27,10.65,12.03,15.42h.02c5.51,3.39,12.79,6.55,21.55,9.42,30.21,9.9,78.02,16.28,131.83,16.28,49.41,0,93.76-5.38,124.06-13.92,2.7-.76,5.29-1.54,7.75-2.35,8.77-2.87,16.05-6.04,21.56-9.43h0c7.76-4.77,12.04-9.97,12.04-15.42"/><path d="m184.582,492.656c-31.354,12.485-50.223,28.58-50.223,46.142,0,9.536,5.564,18.627,15.677,26.969h.022c8.503,7.005,20.213,13.463,34.524,19.159,9.999,3.991,21.269,7.609,33.597,10.788,36.45,9.407,82.181,15.002,131.835,15.002s95.363-5.595,131.807-15.002c10.847-2.79,20.867-5.926,29.924-9.349,1.244-.467,2.473-.942,3.673-1.424,14.326-5.696,26.035-12.161,34.524-19.173h.022c10.114-8.342,15.677-17.433,15.677-26.969,0-17.562-18.869-33.665-50.223-46.15"/><path d="m134.36,592.72c0,39.735,96.554,71.921,215.652,71.921s215.629-32.186,215.629-71.921"/><line x1="134.36" y1="592.72" x2="134.36" y2="538.797"/><line x1="565.64" y1="592.72" x2="565.64" y2="538.797"/><polyline points="481.822 481.901 481.798 481.877 481.775 481.854 350.015 350.026 218.185 218.129"/><polyline points="218.185 481.901 218.231 481.854 350.015 350.026 481.822 218.152"/></g>';
string internal constant HOURGLASS_LOWER_BULB_LARGE =
'<path d="m481.46,481.54v81.01c-2.35.77-4.82,1.51-7.39,2.23-30.3,8.54-74.65,13.92-124.06,13.92-53.6,0-101.24-6.33-131.47-16.16v-81l46.3-46.31h170.33l46.29,46.31Z" fill="url(#SandBottom)"/><path d="m435.17,435.23c0,1.17-.46,2.32-1.33,3.44-7.11,9.08-41.93,15.98-83.81,15.98s-76.7-6.9-83.82-15.98c-.87-1.12-1.33-2.27-1.33-3.44v-.04l8.34-8.35.01-.01c13.72-6.51,42.95-11.02,76.8-11.02s62.97,4.49,76.72,11l8.42,8.42Z" fill="url(#SandTop)"/>';
string internal constant HOURGLASS_LOWER_BULB_SMALL =
'<path d="m481.46,504.101v58.449c-2.35.77-4.82,1.51-7.39,2.23-30.3,8.54-74.65,13.92-124.06,13.92-53.6,0-101.24-6.33-131.47-16.16v-58.439h262.92Z" fill="url(#SandBottom)"/><ellipse cx="350" cy="504.101" rx="131.462" ry="28.108" fill="url(#SandTop)"/>';
string internal constant HOURGLASS_UPPER_BULB =
'<polygon points="350 350.026 415.03 284.978 285 284.978 350 350.026" fill="url(#SandBottom)"/><path d="m416.341,281.975c0,.914-.354,1.809-1.035,2.68-5.542,7.076-32.661,12.45-65.28,12.45-32.624,0-59.738-5.374-65.28-12.45-.681-.872-1.035-1.767-1.035-2.68,0-.914.354-1.808,1.035-2.676,5.542-7.076,32.656-12.45,65.28-12.45,32.619,0,59.738,5.374,65.28,12.45.681.867,1.035,1.762,1.035,2.676Z" fill="url(#SandTop)"/>';
string internal constant NOISE =
'<filter id="Noise"><feFlood x="0" y="0" width="100%" height="100%" flood-color="hsl(230,21%,11%)" flood-opacity="1" result="floodFill"/><feTurbulence baseFrequency=".4" numOctaves="3" result="Noise" type="fractalNoise"/><feBlend in="Noise" in2="floodFill" mode="soft-light"/></filter>';
/// @dev Escape character for "≥".
string internal constant SIGN_GE = "≥";
/// @dev Escape character for ">".
string internal constant SIGN_GT = ">";
/// @dev Escape character for "<".
string internal constant SIGN_LT = "<";
/*//////////////////////////////////////////////////////////////////////////
DATA TYPES
//////////////////////////////////////////////////////////////////////////*/
enum CardType {
PROGRESS,
STATUS,
AMOUNT,
DURATION
}
/*//////////////////////////////////////////////////////////////////////////
COMPONENTS
//////////////////////////////////////////////////////////////////////////*/
function card(CardType cardType, string memory content) internal pure returns (uint256, string memory) {
return card({ cardType: cardType, content: content, circle: "" });
}
function card(
CardType cardType,
string memory content,
string memory circle
)
internal
pure
returns (uint256 width, string memory card_)
{
string memory caption = stringifyCardType(cardType);
// The progress card can have a fixed width because the content is never longer than the caption. The former
// has 6 characters (at most, e.g. "42.09%"), whereas the latter has 8 characters ("Progress").
if (cardType == CardType.PROGRESS) {
// The progress can be 0%, in which case the circle is not rendered.
if (circle.equal("")) {
width = 144; // 2 * 20 (margins) + 8 * 13 (charWidth)
} else {
width = 208; // 3 * 20 (margins) + 8 * 13 (charWidth) + 44 (diameter)
}
}
// For the other cards, the width is calculated dynamically based on the number of characters.
else {
uint256 captionWidth = calculatePixelWidth({ text: caption, largeFont: false });
uint256 contentWidth = calculatePixelWidth({ text: content, largeFont: true });
// Use the greater of the two widths, and add the left and the right margin.
unchecked {
width = Math.max(captionWidth, contentWidth) + 40;
}
}
card_ = string.concat(
'<g id="',
caption,
'" fill="#fff">',
'<rect width="',
width.toString(),
'" height="100" fill-opacity=".03" rx="15" ry="15" stroke="#fff" stroke-opacity=".1" stroke-width="4"/>',
'<text x="20" y="34" font-family="\'Courier New\',Arial,monospace" font-size="22px">',
caption,
"</text>",
'<text x="20" y="72" font-family="\'Courier New\',Arial,monospace" font-size="26px">',
content,
"</text>",
circle,
"</g>"
);
}
function floatingText(string memory offset, string memory text) internal pure returns (string memory) {
return string.concat(
'<textPath startOffset="',
offset,
'" href="#FloatingText" fill="#fff" font-family="\'Courier New\',Arial,monospace" fill-opacity=".8" font-size="26px">',
'<animate additive="sum" attributeName="startOffset" begin="0s" dur="50s" from="0%" repeatCount="indefinite" to="100%"/>',
text,
"</textPath>"
);
}
function gradients(string memory accentColor) internal pure returns (string memory) {
string memory radialGlow = string.concat(
'<radialGradient id="RadialGlow">',
'<stop offset="0%" stop-color="',
accentColor,
'" stop-opacity=".6"/>',
'<stop offset="100%" stop-color="',
BACKGROUND_COLOR,
'" stop-opacity="0"/>',
"</radialGradient>"
);
string memory sandTop = string.concat(
'<linearGradient id="SandTop" x1="0%" y1="0%">',
'<stop offset="0%" stop-color="',
accentColor,
'"/>',
'<stop offset="100%" stop-color="',
BACKGROUND_COLOR,
'"/>',
"</linearGradient>"
);
string memory sandBottom = string.concat(
'<linearGradient id="SandBottom" x1="100%" y1="100%">',
'<stop offset="10%" stop-color="',
BACKGROUND_COLOR,
'"/>',
'<stop offset="100%" stop-color="',
accentColor,
'"/>',
'<animate attributeName="x1" dur="6s" repeatCount="indefinite" values="30%;60%;120%;60%;30%;"/>',
"</linearGradient>"
);
// Needs to be declared last so that the stroke is painted on top of the sand.
string memory hourglassStroke = string.concat(
'<linearGradient id="HourglassStroke" gradientTransform="rotate(90)" gradientUnits="userSpaceOnUse">',
'<stop offset="50%" stop-color="',
accentColor,
'"/>',
'<stop offset="80%" stop-color="',
BACKGROUND_COLOR,
'"/>',
"</linearGradient>"
);
return string.concat(radialGlow, sandTop, sandBottom, hourglassStroke);
}
function hourglass(string memory status) internal pure returns (string memory) {
bool settledOrDepleted = status.equal("Settled") || status.equal("Depleted");
return string.concat(
'<g id="Hourglass">',
HOURGLASS_BACKGROUND_CIRCLE,
HOURGLASS_FILL,
settledOrDepleted ? "" : HOURGLASS_UPPER_BULB, // empty or filled
settledOrDepleted ? HOURGLASS_LOWER_BULB_LARGE : HOURGLASS_LOWER_BULB_SMALL,
HOURGLASS_STROKE, // needs to be declared last so that the stroke is painted on top of the sand
"</g>"
);
}
function progressCircle(
uint256 progressNumerical,
string memory accentColor
)
internal
pure
returns (string memory)
{
if (progressNumerical == 0) {
return "";
}
return string.concat(
'<g fill="none">',
'<circle cx="166" cy="50" r="22" stroke="',
BACKGROUND_COLOR,
'" stroke-width="10"/>',
'<circle cx="166" cy="50" pathLength="10000" r="22" stroke="',
accentColor,
'" stroke-dasharray="10000" stroke-dashoffset="',
(10_000 - progressNumerical).toString(),
'" stroke-linecap="round" stroke-width="5" transform="rotate(-90)" transform-origin="166 50"/>',
"</g>"
);
}
/*//////////////////////////////////////////////////////////////////////////
HELPERS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Calculates the pixel width of the provided string.
/// @dev Notes:
/// - A factor of ~0.6 is applied to the two font sizes used in the SVG (26px and 22px) to approximate the average
/// character width.
/// - It is assumed that escaped characters are placed at the beginning of `text`.
/// - It is further assumed that there is no other semicolon in `text`.
function calculatePixelWidth(string memory text, bool largeFont) internal pure returns (uint256 width) {
uint256 length = bytes(text).length;
if (length == 0) {
return 0;
}
unchecked {
uint256 charWidth = largeFont ? 16 : 13;
uint256 semicolonIndex;
for (uint256 i = 0; i < length; ++i) {
if (bytes(text)[i] == ";") {
semicolonIndex = i;
}
width += charWidth;
}
// Account for escaped characters (such as ≥).
width -= charWidth * semicolonIndex;
}
}
/// @notice Retrieves the card type as a string.
function stringifyCardType(CardType cardType) internal pure returns (string memory) {
if (cardType == CardType.PROGRESS) {
return "Progress";
} else if (cardType == CardType.STATUS) {
return "Status";
} else if (cardType == CardType.AMOUNT) {
return "Amount";
} else {
return "Duration";
}
}
}// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;
import { IERC721Metadata } from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
/// @title ISablierV2NFTDescriptor
/// @notice This contract generates the URI describing the Sablier V2 stream NFTs.
/// @dev Inspired by Uniswap V3 Positions NFTs.
interface ISablierV2NFTDescriptor {
/// @notice Produces the URI describing a particular stream NFT.
/// @dev This is a data URI with the JSON contents directly inlined.
/// @param sablier The address of the Sablier contract the stream was created in.
/// @param streamId The ID of the stream for which to produce a description.
/// @return uri The URI of the ERC721-compliant metadata.
function tokenURI(IERC721Metadata sablier, uint256 streamId) external view returns (string memory uri);
}// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;
import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { UD2x18 } from "@prb/math/src/UD2x18.sol";
import { UD60x18 } from "@prb/math/src/UD60x18.sol";
// DataTypes.sol
//
// This file defines all structs used in V2 Core, most of which are organized under three namespaces:
//
// - Lockup
// - LockupDynamic
// - LockupLinear
// - LockupTranched
//
// You will notice that some structs contain "slot" annotations - they are used to indicate the
// storage layout of the struct. It is more gas efficient to group small data types together so
// that they fit in a single 32-byte slot.
/// @notice Struct encapsulating the broker parameters passed to the create functions. Both can be set to zero.
/// @param account The address receiving the broker's fee.
/// @param fee The broker's percentage fee from the total amount, denoted as a fixed-point number where 1e18 is 100%.
struct Broker {
address account;
UD60x18 fee;
}
/// @notice Namespace for the structs used in both {SablierV2LockupLinear} and {SablierV2LockupDynamic}.
library Lockup {
/// @notice Struct encapsulating the deposit, withdrawn, and refunded amounts, both denoted in units of the asset's
/// decimals.
/// @dev Because the deposited and the withdrawn amount are often read together, declaring them in the same slot
/// saves gas.
/// @param deposited The initial amount deposited in the stream, net of broker fee.
/// @param withdrawn The cumulative amount withdrawn from the stream.
/// @param refunded The amount refunded to the sender. Unless the stream was canceled, this is always zero.
struct Amounts {
// slot 0
uint128 deposited;
uint128 withdrawn;
// slot 1
uint128 refunded;
}
/// @notice Struct encapsulating the deposit amount and the broker fee amount, both denoted in units of the asset's
/// decimals.
/// @param deposit The amount to deposit in the stream.
/// @param brokerFee The broker fee amount.
struct CreateAmounts {
uint128 deposit;
uint128 brokerFee;
}
/// @notice Enum representing the different statuses of a stream.
/// @custom:value0 PENDING Stream created but not started; assets are in a pending state.
/// @custom:value1 STREAMING Active stream where assets are currently being streamed.
/// @custom:value2 SETTLED All assets have been streamed; recipient is due to withdraw them.
/// @custom:value3 CANCELED Canceled stream; remaining assets await recipient's withdrawal.
/// @custom:value4 DEPLETED Depleted stream; all assets have been withdrawn and/or refunded.
enum Status {
PENDING,
STREAMING,
SETTLED,
CANCELED,
DEPLETED
}
/// @notice A common data structure to be stored in all {SablierV2Lockup} models.
/// @dev The fields are arranged like this to save gas via tight variable packing.
/// @param sender The address distributing the assets, with the ability to cancel the stream.
/// @param startTime The Unix timestamp indicating the stream's start.
/// @param endTime The Unix timestamp indicating the stream's end.
/// @param isCancelable Boolean indicating if the stream is cancelable.
/// @param wasCanceled Boolean indicating if the stream was canceled.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param isDepleted Boolean indicating if the stream is depleted.
/// @param isStream Boolean indicating if the struct entity exists.
/// @param isTransferable Boolean indicating if the stream NFT is transferable.
/// @param amounts Struct containing the deposit, withdrawn, and refunded amounts, both denoted in units of the
/// asset's decimals.
struct Stream {
// slot 0
address sender;
uint40 startTime;
uint40 endTime;
bool isCancelable;
bool wasCanceled;
// slot 1
IERC20 asset;
bool isDepleted;
bool isStream;
bool isTransferable;
// slot 2 and 3
Lockup.Amounts amounts;
}
}
/// @notice Namespace for the structs used in {SablierV2LockupDynamic}.
library LockupDynamic {
/// @notice Struct encapsulating the parameters of the {SablierV2LockupDynamic.createWithDurations} function.
/// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be
/// the same as `msg.sender`.
/// @param recipient The address receiving the assets.
/// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any
/// broker fee, both denoted in units of the asset's decimals.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param cancelable Indicates if the stream is cancelable.
/// @param transferable Indicates if the stream NFT is transferable.
/// @param segments Segments with durations used to compose the dynamic distribution function. Timestamps are
/// calculated by starting from `block.timestamp` and adding each duration to the previous timestamp.
/// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the
/// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.
struct CreateWithDurations {
address sender;
address recipient;
uint128 totalAmount;
IERC20 asset;
bool cancelable;
bool transferable;
SegmentWithDuration[] segments;
Broker broker;
}
/// @notice Struct encapsulating the parameters of the {SablierV2LockupDynamic.createWithTimestamps} function.
/// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be
/// the same as `msg.sender`.
/// @param recipient The address receiving the assets.
/// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any
/// broker fee, both denoted in units of the asset's decimals.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param cancelable Indicates if the stream is cancelable.
/// @param transferable Indicates if the stream NFT is transferable.
/// @param startTime The Unix timestamp indicating the stream's start.
/// @param segments Segments used to compose the dynamic distribution function.
/// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the
/// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.
struct CreateWithTimestamps {
address sender;
address recipient;
uint128 totalAmount;
IERC20 asset;
bool cancelable;
bool transferable;
uint40 startTime;
Segment[] segments;
Broker broker;
}
/// @notice Segment struct used in the Lockup Dynamic stream.
/// @param amount The amount of assets to be streamed in the segment, denoted in units of the asset's decimals.
/// @param exponent The exponent of the segment, denoted as a fixed-point number.
/// @param timestamp The Unix timestamp indicating the segment's end.
struct Segment {
// slot 0
uint128 amount;
UD2x18 exponent;
uint40 timestamp;
}
/// @notice Segment struct used at runtime in {SablierV2LockupDynamic.createWithDurations}.
/// @param amount The amount of assets to be streamed in the segment, denoted in units of the asset's decimals.
/// @param exponent The exponent of the segment, denoted as a fixed-point number.
/// @param duration The time difference in seconds between the segment and the previous one.
struct SegmentWithDuration {
uint128 amount;
UD2x18 exponent;
uint40 duration;
}
/// @notice Struct encapsulating the full details of a stream.
/// @dev Extends `Lockup.Stream` by including the recipient and the segments.
struct StreamLD {
address sender;
address recipient;
uint40 startTime;
uint40 endTime;
bool isCancelable;
bool wasCanceled;
IERC20 asset;
bool isDepleted;
bool isStream;
bool isTransferable;
Lockup.Amounts amounts;
Segment[] segments;
}
/// @notice Struct encapsulating the LockupDynamic timestamps.
/// @param start The Unix timestamp indicating the stream's start.
/// @param end The Unix timestamp indicating the stream's end.
struct Timestamps {
uint40 start;
uint40 end;
}
}
/// @notice Namespace for the structs used in {SablierV2LockupLinear}.
library LockupLinear {
/// @notice Struct encapsulating the parameters of the {SablierV2LockupLinear.createWithDurations} function.
/// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be
/// the same as `msg.sender`.
/// @param recipient The address receiving the assets.
/// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any
/// broker fee, both denoted in units of the asset's decimals.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param cancelable Indicates if the stream is cancelable.
/// @param transferable Indicates if the stream NFT is transferable.
/// @param durations Struct containing (i) cliff period duration and (ii) total stream duration, both in seconds.
/// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the
/// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.
struct CreateWithDurations {
address sender;
address recipient;
uint128 totalAmount;
IERC20 asset;
bool cancelable;
bool transferable;
Durations durations;
Broker broker;
}
/// @notice Struct encapsulating the parameters of the {SablierV2LockupLinear.createWithTimestamps} function.
/// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be
/// the same as `msg.sender`.
/// @param recipient The address receiving the assets.
/// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any
/// broker fee, both denoted in units of the asset's decimals.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param cancelable Indicates if the stream is cancelable.
/// @param transferable Indicates if the stream NFT is transferable.
/// @param timestamps Struct containing (i) the stream's start time, (ii) cliff time, and (iii) end time, all as
/// Unix timestamps.
/// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the
/// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.
struct CreateWithTimestamps {
address sender;
address recipient;
uint128 totalAmount;
IERC20 asset;
bool cancelable;
bool transferable;
Timestamps timestamps;
Broker broker;
}
/// @notice Struct encapsulating the cliff duration and the total duration.
/// @param cliff The cliff duration in seconds.
/// @param total The total duration in seconds.
struct Durations {
uint40 cliff;
uint40 total;
}
/// @notice Struct encapsulating the full details of a stream.
/// @dev Extends `Lockup.Stream` by including the recipient and the cliff time.
struct StreamLL {
address sender;
address recipient;
uint40 startTime;
bool isCancelable;
bool wasCanceled;
IERC20 asset;
uint40 endTime;
bool isDepleted;
bool isStream;
bool isTransferable;
Lockup.Amounts amounts;
uint40 cliffTime;
}
/// @notice Struct encapsulating the LockupLinear timestamps.
/// @param start The Unix timestamp for the stream's start.
/// @param cliff The Unix timestamp for the cliff period's end. A value of zero means there is no cliff.
/// @param end The Unix timestamp for the stream's end.
struct Timestamps {
uint40 start;
uint40 cliff;
uint40 end;
}
}
/// @notice Namespace for the structs used in {SablierV2LockupTranched}.
library LockupTranched {
/// @notice Struct encapsulating the parameters of the {SablierV2LockupTranched.createWithDurations} function.
/// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be
/// the same as `msg.sender`.
/// @param recipient The address receiving the assets.
/// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any
/// broker fee, both denoted in units of the asset's decimals.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param cancelable Indicates if the stream is cancelable.
/// @param transferable Indicates if the stream NFT is transferable.
/// @param tranches Tranches with durations used to compose the tranched distribution function. Timestamps are
/// calculated by starting from `block.timestamp` and adding each duration to the previous timestamp.
/// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the
/// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.
struct CreateWithDurations {
address sender;
address recipient;
uint128 totalAmount;
IERC20 asset;
bool cancelable;
bool transferable;
TrancheWithDuration[] tranches;
Broker broker;
}
/// @notice Struct encapsulating the parameters of the {SablierV2LockupTranched.createWithTimestamps} function.
/// @param sender The address distributing the assets, with the ability to cancel the stream. It doesn't have to be
/// the same as `msg.sender`.
/// @param recipient The address receiving the assets.
/// @param totalAmount The total amount of ERC-20 assets to be distributed, including the stream deposit and any
/// broker fee, both denoted in units of the asset's decimals.
/// @param asset The contract address of the ERC-20 asset to be distributed.
/// @param cancelable Indicates if the stream is cancelable.
/// @param transferable Indicates if the stream NFT is transferable.
/// @param startTime The Unix timestamp indicating the stream's start.
/// @param tranches Tranches used to compose the tranched distribution function.
/// @param broker Struct containing (i) the address of the broker assisting in creating the stream, and (ii) the
/// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.
struct CreateWithTimestamps {
address sender;
address recipient;
uint128 totalAmount;
IERC20 asset;
bool cancelable;
bool transferable;
uint40 startTime;
Tranche[] tranches;
Broker broker;
}
/// @notice Struct encapsulating the full details of a stream.
/// @dev Extends `Lockup.Stream` by including the recipient and the tranches.
struct StreamLT {
address sender;
address recipient;
uint40 startTime;
uint40 endTime;
bool isCancelable;
bool wasCanceled;
IERC20 asset;
bool isDepleted;
bool isStream;
bool isTransferable;
Lockup.Amounts amounts;
Tranche[] tranches;
}
/// @notice Struct encapsulating the LockupTranched timestamps.
/// @param start The Unix timestamp indicating the stream's start.
/// @param end The Unix timestamp indicating the stream's end.
struct Timestamps {
uint40 start;
uint40 end;
}
/// @notice Tranche struct used in the Lockup Tranched stream.
/// @param amount The amount of assets to be unlocked in the tranche, denoted in units of the asset's decimals.
/// @param timestamp The Unix timestamp indicating the tranche's end.
struct Tranche {
// slot 0
uint128 amount;
uint40 timestamp;
}
/// @notice Tranche struct used at runtime in {SablierV2LockupTranched.createWithDurations}.
/// @param amount The amount of assets to be unlocked in the tranche, denoted in units of the asset's decimals.
/// @param duration The time difference in seconds between the tranche and the previous one.
struct TrancheWithDuration {
uint128 amount;
uint40 duration;
}
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/extensions/IERC721Metadata.sol)
pragma solidity ^0.8.20;
import {IERC721} from "../IERC721.sol";
/**
* @title ERC-721 Non-Fungible Token Standard, optional metadata extension
* @dev See https://eips.ethereum.org/EIPS/eip-721
*/
interface IERC721Metadata is IERC721 {
/**
* @dev Returns the token collection name.
*/
function name() external view returns (string memory);
/**
* @dev Returns the token collection symbol.
*/
function symbol() external view returns (string memory);
/**
* @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
*/
function tokenURI(uint256 tokenId) external view returns (string memory);
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.2) (utils/Base64.sol)
pragma solidity ^0.8.20;
/**
* @dev Provides a set of functions to operate with Base64 strings.
*/
library Base64 {
/**
* @dev Base64 Encoding/Decoding Table
*/
string internal constant _TABLE = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
/**
* @dev Converts a `bytes` to its Bytes64 `string` representation.
*/
function encode(bytes memory data) internal pure returns (string memory) {
/**
* Inspired by Brecht Devos (Brechtpd) implementation - MIT licence
* https://github.com/Brechtpd/base64/blob/e78d9fd951e7b0977ddca77d92dc85183770daf4/base64.sol
*/
if (data.length == 0) return "";
// Loads the table into memory
string memory table = _TABLE;
// Encoding takes 3 bytes chunks of binary data from `bytes` data parameter
// and split into 4 numbers of 6 bits.
// The final Base64 length should be `bytes` data length multiplied by 4/3 rounded up
// - `data.length + 2` -> Round up
// - `/ 3` -> Number of 3-bytes chunks
// - `4 *` -> 4 characters for each chunk
string memory result = new string(4 * ((data.length + 2) / 3));
/// @solidity memory-safe-assembly
assembly {
// Prepare the lookup table (skip the first "length" byte)
let tablePtr := add(table, 1)
// Prepare result pointer, jump over length
let resultPtr := add(result, 0x20)
let dataPtr := data
let endPtr := add(data, mload(data))
// In some cases, the last iteration will read bytes after the end of the data. We cache the value, and
// set it to zero to make sure no dirty bytes are read in that section.
let afterPtr := add(endPtr, 0x20)
let afterCache := mload(afterPtr)
mstore(afterPtr, 0x00)
// Run over the input, 3 bytes at a time
for {
} lt(dataPtr, endPtr) {
} {
// Advance 3 bytes
dataPtr := add(dataPtr, 3)
let input := mload(dataPtr)
// To write each character, shift the 3 byte (24 bits) chunk
// 4 times in blocks of 6 bits for each character (18, 12, 6, 0)
// and apply logical AND with 0x3F to bitmask the least significant 6 bits.
// Use this as an index into the lookup table, mload an entire word
// so the desired character is in the least significant byte, and
// mstore8 this least significant byte into the result and continue.
mstore8(resultPtr, mload(add(tablePtr, and(shr(18, input), 0x3F))))
resultPtr := add(resultPtr, 1) // Advance
mstore8(resultPtr, mload(add(tablePtr, and(shr(12, input), 0x3F))))
resultPtr := add(resultPtr, 1) // Advance
mstore8(resultPtr, mload(add(tablePtr, and(shr(6, input), 0x3F))))
resultPtr := add(resultPtr, 1) // Advance
mstore8(resultPtr, mload(add(tablePtr, and(input, 0x3F))))
resultPtr := add(resultPtr, 1) // Advance
}
// Reset the value that was cached
mstore(afterPtr, afterCache)
// When data `bytes` is not exactly 3 bytes long
// it is padded with `=` characters at the end
switch mod(mload(data), 3)
case 1 {
mstore8(sub(resultPtr, 1), 0x3d)
mstore8(sub(resultPtr, 2), 0x3d)
}
case 2 {
mstore8(sub(resultPtr, 1), 0x3d)
}
}
return result;
}
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/Strings.sol)
pragma solidity ^0.8.20;
import {Math} from "./math/Math.sol";
import {SignedMath} from "./math/SignedMath.sol";
/**
* @dev String operations.
*/
library Strings {
bytes16 private constant HEX_DIGITS = "0123456789abcdef";
uint8 private constant ADDRESS_LENGTH = 20;
/**
* @dev The `value` string doesn't fit in the specified `length`.
*/
error StringsInsufficientHexLength(uint256 value, uint256 length);
/**
* @dev Converts a `uint256` to its ASCII `string` decimal representation.
*/
function toString(uint256 value) internal pure returns (string memory) {
unchecked {
uint256 length = Math.log10(value) + 1;
string memory buffer = new string(length);
uint256 ptr;
/// @solidity memory-safe-assembly
assembly {
ptr := add(buffer, add(32, length))
}
while (true) {
ptr--;
/// @solidity memory-safe-assembly
assembly {
mstore8(ptr, byte(mod(value, 10), HEX_DIGITS))
}
value /= 10;
if (value == 0) break;
}
return buffer;
}
}
/**
* @dev Converts a `int256` to its ASCII `string` decimal representation.
*/
function toStringSigned(int256 value) internal pure returns (string memory) {
return string.concat(value < 0 ? "-" : "", toString(SignedMath.abs(value)));
}
/**
* @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
*/
function toHexString(uint256 value) internal pure returns (string memory) {
unchecked {
return toHexString(value, Math.log256(value) + 1);
}
}
/**
* @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
*/
function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
uint256 localValue = value;
bytes memory buffer = new bytes(2 * length + 2);
buffer[0] = "0";
buffer[1] = "x";
for (uint256 i = 2 * length + 1; i > 1; --i) {
buffer[i] = HEX_DIGITS[localValue & 0xf];
localValue >>= 4;
}
if (localValue != 0) {
revert StringsInsufficientHexLength(value, length);
}
return string(buffer);
}
/**
* @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal
* representation.
*/
function toHexString(address addr) internal pure returns (string memory) {
return toHexString(uint256(uint160(addr)), ADDRESS_LENGTH);
}
/**
* @dev Returns true if the two strings are equal.
*/
function equal(string memory a, string memory b) internal pure returns (bool) {
return bytes(a).length == bytes(b).length && keccak256(bytes(a)) == keccak256(bytes(b));
}
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/extensions/IERC20Metadata.sol)
pragma solidity ^0.8.20;
import {IERC20} from "../IERC20.sol";
/**
* @dev Interface for the optional metadata functions from the ERC20 standard.
*/
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);
}// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;
/// @title IAdminable
/// @notice Contract module that provides a basic access control mechanism, with an admin that can be
/// granted exclusive access to specific functions. The inheriting contract must set the initial admin
/// in the constructor.
interface IAdminable {
/*//////////////////////////////////////////////////////////////////////////
EVENTS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Emitted when the admin is transferred.
/// @param oldAdmin The address of the old admin.
/// @param newAdmin The address of the new admin.
event TransferAdmin(address indexed oldAdmin, address indexed newAdmin);
/*//////////////////////////////////////////////////////////////////////////
CONSTANT FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice The address of the admin account or contract.
function admin() external view returns (address);
/*//////////////////////////////////////////////////////////////////////////
NON-CONSTANT FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Transfers the contract admin to a new address.
///
/// @dev Notes:
/// - Does not revert if the admin is the same.
/// - This function can potentially leave the contract without an admin, thereby removing any
/// functionality that is only available to the admin.
///
/// Requirements:
/// - `msg.sender` must be the contract admin.
///
/// @param newAdmin The address of the new admin.
function transferAdmin(address newAdmin) external;
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC4906.sol)
pragma solidity ^0.8.20;
import {IERC165} from "./IERC165.sol";
import {IERC721} from "./IERC721.sol";
/// @title EIP-721 Metadata Update Extension
interface IERC4906 is IERC165, IERC721 {
/// @dev This event emits when the metadata of a token is changed.
/// So that the third-party platforms such as NFT market could
/// timely update the images and related attributes of the NFT.
event MetadataUpdate(uint256 _tokenId);
/// @dev This event emits when the metadata of a range of tokens is changed.
/// So that the third-party platforms such as NFT market could
/// timely update the images and related attributes of the NFTs.
event BatchMetadataUpdate(uint256 _fromTokenId, uint256 _toTokenId);
}// SPDX-License-Identifier: MIT pragma solidity >=0.8.19; /* ██████╗ ██████╗ ██████╗ ███╗ ███╗ █████╗ ████████╗██╗ ██╗ ██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║ ██║ ██████╔╝██████╔╝██████╔╝██╔████╔██║███████║ ██║ ███████║ ██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║ ██║ ██╔══██║ ██║ ██║ ██║██████╔╝██║ ╚═╝ ██║██║ ██║ ██║ ██║ ██║ ╚═╝ ╚═╝ ╚═╝╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝ ██╗ ██╗██████╗ ██████╗ ██████╗ ██╗ ██╗ ██╗ █████╗ ██║ ██║██╔══██╗██╔════╝ ██╔═████╗╚██╗██╔╝███║██╔══██╗ ██║ ██║██║ ██║███████╗ ██║██╔██║ ╚███╔╝ ╚██║╚█████╔╝ ██║ ██║██║ ██║██╔═══██╗████╔╝██║ ██╔██╗ ██║██╔══██╗ ╚██████╔╝██████╔╝╚██████╔╝╚██████╔╝██╔╝ ██╗ ██║╚█████╔╝ ╚═════╝ ╚═════╝ ╚═════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚════╝ */ import "./ud60x18/Casting.sol"; import "./ud60x18/Constants.sol"; import "./ud60x18/Conversions.sol"; import "./ud60x18/Errors.sol"; import "./ud60x18/Helpers.sol"; import "./ud60x18/Math.sol"; import "./ud60x18/ValueType.sol";
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/IERC20.sol)
pragma solidity ^0.8.20;
/**
* @dev Interface of the ERC20 standard as defined in the EIP.
*/
interface IERC20 {
/**
* @dev Emitted when `value` tokens are moved from one account (`from`) to
* another (`to`).
*
* Note that `value` may be zero.
*/
event Transfer(address indexed from, address indexed to, uint256 value);
/**
* @dev Emitted when the allowance of a `spender` for an `owner` is set by
* a call to {approve}. `value` is the new allowance.
*/
event Approval(address indexed owner, address indexed spender, uint256 value);
/**
* @dev Returns the value of tokens in existence.
*/
function totalSupply() external view returns (uint256);
/**
* @dev Returns the value of tokens owned by `account`.
*/
function balanceOf(address account) external view returns (uint256);
/**
* @dev Moves a `value` amount of tokens from the caller's account to `to`.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transfer(address to, uint256 value) 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 a `value` amount of tokens 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 value) external returns (bool);
/**
* @dev Moves a `value` amount of tokens from `from` to `to` using the
* allowance mechanism. `value` is then deducted from the caller's
* allowance.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transferFrom(address from, address to, uint256 value) external returns (bool);
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol)
pragma solidity ^0.8.20;
/**
* @dev Standard math utilities missing in the Solidity language.
*/
library Math {
/**
* @dev Muldiv operation overflow.
*/
error MathOverflowedMulDiv();
enum Rounding {
Floor, // Toward negative infinity
Ceil, // Toward positive infinity
Trunc, // Toward zero
Expand // Away from zero
}
/**
* @dev Returns the addition of two unsigned integers, with an overflow flag.
*/
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 subtraction of two unsigned integers, with an overflow flag.
*/
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.
*/
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.
*/
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.
*/
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 largest of two numbers.
*/
function max(uint256 a, uint256 b) internal pure returns (uint256) {
return a > b ? a : b;
}
/**
* @dev Returns the smallest of two numbers.
*/
function min(uint256 a, uint256 b) internal pure returns (uint256) {
return a < b ? a : b;
}
/**
* @dev Returns the average of two numbers. The result is rounded towards
* zero.
*/
function average(uint256 a, uint256 b) internal pure returns (uint256) {
// (a + b) / 2 can overflow.
return (a & b) + (a ^ b) / 2;
}
/**
* @dev Returns the ceiling of the division of two numbers.
*
* This differs from standard division with `/` in that it rounds towards infinity instead
* of rounding towards zero.
*/
function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
if (b == 0) {
// Guarantee the same behavior as in a regular Solidity division.
return a / b;
}
// (a + b - 1) / b can overflow on addition, so we distribute.
return a == 0 ? 0 : (a - 1) / b + 1;
}
/**
* @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or
* denominator == 0.
* @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv) with further edits by
* Uniswap Labs also under MIT license.
*/
function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
unchecked {
// 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
// use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
// variables such that product = prod1 * 2^256 + prod0.
uint256 prod0 = x * y; // Least significant 256 bits of the product
uint256 prod1; // Most significant 256 bits of the product
assembly {
let mm := mulmod(x, y, not(0))
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
// Handle non-overflow cases, 256 by 256 division.
if (prod1 == 0) {
// Solidity will revert if denominator == 0, unlike the div opcode on its own.
// The surrounding unchecked block does not change this fact.
// See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
return prod0 / denominator;
}
// Make sure the result is less than 2^256. Also prevents denominator == 0.
if (denominator <= prod1) {
revert MathOverflowedMulDiv();
}
///////////////////////////////////////////////
// 512 by 256 division.
///////////////////////////////////////////////
// Make division exact by subtracting the remainder from [prod1 prod0].
uint256 remainder;
assembly {
// Compute remainder using mulmod.
remainder := mulmod(x, y, denominator)
// Subtract 256 bit number from 512 bit number.
prod1 := sub(prod1, gt(remainder, prod0))
prod0 := sub(prod0, remainder)
}
// Factor powers of two out of denominator and compute largest power of two divisor of denominator.
// Always >= 1. See https://cs.stackexchange.com/q/138556/92363.
uint256 twos = denominator & (0 - denominator);
assembly {
// Divide denominator by twos.
denominator := div(denominator, twos)
// Divide [prod1 prod0] by twos.
prod0 := div(prod0, twos)
// Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
twos := add(div(sub(0, twos), twos), 1)
}
// Shift in bits from prod1 into prod0.
prod0 |= prod1 * twos;
// Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
// that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
// four bits. That is, denominator * inv = 1 mod 2^4.
uint256 inverse = (3 * denominator) ^ 2;
// Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also
// works in modular arithmetic, doubling the correct bits in each step.
inverse *= 2 - denominator * inverse; // inverse mod 2^8
inverse *= 2 - denominator * inverse; // inverse mod 2^16
inverse *= 2 - denominator * inverse; // inverse mod 2^32
inverse *= 2 - denominator * inverse; // inverse mod 2^64
inverse *= 2 - denominator * inverse; // inverse mod 2^128
inverse *= 2 - denominator * inverse; // inverse mod 2^256
// Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
// This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
// less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
// is no longer required.
result = prod0 * inverse;
return result;
}
}
/**
* @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
*/
function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
uint256 result = mulDiv(x, y, denominator);
if (unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0) {
result += 1;
}
return result;
}
/**
* @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded
* towards zero.
*
* Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
*/
function sqrt(uint256 a) internal pure returns (uint256) {
if (a == 0) {
return 0;
}
// For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
//
// We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
// `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
//
// This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
// → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
// → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
//
// Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
uint256 result = 1 << (log2(a) >> 1);
// At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
// since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
// every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
// into the expected uint128 result.
unchecked {
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
result = (result + a / result) >> 1;
return min(result, a / result);
}
}
/**
* @notice Calculates sqrt(a), following the selected rounding direction.
*/
function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
unchecked {
uint256 result = sqrt(a);
return result + (unsignedRoundsUp(rounding) && result * result < a ? 1 : 0);
}
}
/**
* @dev Return the log in base 2 of a positive value rounded towards zero.
* Returns 0 if given 0.
*/
function log2(uint256 value) internal pure returns (uint256) {
uint256 result = 0;
unchecked {
if (value >> 128 > 0) {
value >>= 128;
result += 128;
}
if (value >> 64 > 0) {
value >>= 64;
result += 64;
}
if (value >> 32 > 0) {
value >>= 32;
result += 32;
}
if (value >> 16 > 0) {
value >>= 16;
result += 16;
}
if (value >> 8 > 0) {
value >>= 8;
result += 8;
}
if (value >> 4 > 0) {
value >>= 4;
result += 4;
}
if (value >> 2 > 0) {
value >>= 2;
result += 2;
}
if (value >> 1 > 0) {
result += 1;
}
}
return result;
}
/**
* @dev Return the log in base 2, following the selected rounding direction, of a positive value.
* Returns 0 if given 0.
*/
function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
unchecked {
uint256 result = log2(value);
return result + (unsignedRoundsUp(rounding) && 1 << result < value ? 1 : 0);
}
}
/**
* @dev Return the log in base 10 of a positive value rounded towards zero.
* Returns 0 if given 0.
*/
function log10(uint256 value) internal pure returns (uint256) {
uint256 result = 0;
unchecked {
if (value >= 10 ** 64) {
value /= 10 ** 64;
result += 64;
}
if (value >= 10 ** 32) {
value /= 10 ** 32;
result += 32;
}
if (value >= 10 ** 16) {
value /= 10 ** 16;
result += 16;
}
if (value >= 10 ** 8) {
value /= 10 ** 8;
result += 8;
}
if (value >= 10 ** 4) {
value /= 10 ** 4;
result += 4;
}
if (value >= 10 ** 2) {
value /= 10 ** 2;
result += 2;
}
if (value >= 10 ** 1) {
result += 1;
}
}
return result;
}
/**
* @dev Return the log in base 10, following the selected rounding direction, of a positive value.
* Returns 0 if given 0.
*/
function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
unchecked {
uint256 result = log10(value);
return result + (unsignedRoundsUp(rounding) && 10 ** result < value ? 1 : 0);
}
}
/**
* @dev Return the log in base 256 of a positive value rounded towards zero.
* Returns 0 if given 0.
*
* Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
*/
function log256(uint256 value) internal pure returns (uint256) {
uint256 result = 0;
unchecked {
if (value >> 128 > 0) {
value >>= 128;
result += 16;
}
if (value >> 64 > 0) {
value >>= 64;
result += 8;
}
if (value >> 32 > 0) {
value >>= 32;
result += 4;
}
if (value >> 16 > 0) {
value >>= 16;
result += 2;
}
if (value >> 8 > 0) {
result += 1;
}
}
return result;
}
/**
* @dev Return the log in base 256, following the selected rounding direction, of a positive value.
* Returns 0 if given 0.
*/
function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
unchecked {
uint256 result = log256(value);
return result + (unsignedRoundsUp(rounding) && 1 << (result << 3) < value ? 1 : 0);
}
}
/**
* @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.
*/
function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {
return uint8(rounding) % 2 == 1;
}
}// SPDX-License-Identifier: MIT pragma solidity >=0.8.19; /* ██████╗ ██████╗ ██████╗ ███╗ ███╗ █████╗ ████████╗██╗ ██╗ ██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║ ██║ ██████╔╝██████╔╝██████╔╝██╔████╔██║███████║ ██║ ███████║ ██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║ ██║ ██╔══██║ ██║ ██║ ██║██████╔╝██║ ╚═╝ ██║██║ ██║ ██║ ██║ ██║ ╚═╝ ╚═╝ ╚═╝╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝ ██╗ ██╗██████╗ ██████╗ ██╗ ██╗ ██╗ █████╗ ██║ ██║██╔══██╗╚════██╗╚██╗██╔╝███║██╔══██╗ ██║ ██║██║ ██║ █████╔╝ ╚███╔╝ ╚██║╚█████╔╝ ██║ ██║██║ ██║██╔═══╝ ██╔██╗ ██║██╔══██╗ ╚██████╔╝██████╔╝███████╗██╔╝ ██╗ ██║╚█████╔╝ ╚═════╝ ╚═════╝ ╚══════╝╚═╝ ╚═╝ ╚═╝ ╚════╝ */ import "./ud2x18/Casting.sol"; import "./ud2x18/Constants.sol"; import "./ud2x18/Errors.sol"; import "./ud2x18/ValueType.sol";
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/IERC721.sol)
pragma solidity ^0.8.20;
import {IERC165} from "../../utils/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`.
*
* 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;
/**
* @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 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: Note that the caller is responsible to confirm that the recipient is capable of receiving ERC721
* or else they may be permanently lost. Usage of {safeTransferFrom} prevents loss, though the caller must
* understand this adds an external call which potentially creates a reentrancy vulnerability.
*
* 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 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 address zero.
*
* Emits an {ApprovalForAll} event.
*/
function setApprovalForAll(address operator, bool approved) external;
/**
* @dev Returns the account approved for `tokenId` token.
*
* Requirements:
*
* - `tokenId` must exist.
*/
function getApproved(uint256 tokenId) external view returns (address operator);
/**
* @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);
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/SignedMath.sol)
pragma solidity ^0.8.20;
/**
* @dev Standard signed math utilities missing in the Solidity language.
*/
library SignedMath {
/**
* @dev Returns the largest of two signed numbers.
*/
function max(int256 a, int256 b) internal pure returns (int256) {
return a > b ? a : b;
}
/**
* @dev Returns the smallest of two signed numbers.
*/
function min(int256 a, int256 b) internal pure returns (int256) {
return a < b ? a : b;
}
/**
* @dev Returns the average of two signed numbers without overflow.
* The result is rounded towards zero.
*/
function average(int256 a, int256 b) internal pure returns (int256) {
// Formula from the book "Hacker's Delight"
int256 x = (a & b) + ((a ^ b) >> 1);
return x + (int256(uint256(x) >> 255) & (a ^ b));
}
/**
* @dev Returns the absolute unsigned value of a signed value.
*/
function abs(int256 n) internal pure returns (uint256) {
unchecked {
// must be unchecked in order to support `n = type(int256).min`
return uint256(n >= 0 ? n : -n);
}
}
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC165.sol)
pragma solidity ^0.8.20;
import {IERC165} from "../utils/introspection/IERC165.sol";// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC721.sol)
pragma solidity ^0.8.20;
import {IERC721} from "../token/ERC721/IERC721.sol";// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Errors.sol" as CastingErrors;
import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_SD59x18 } from "../sd59x18/Constants.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "./ValueType.sol";
/// @notice Casts a UD60x18 number into SD1x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(UD60x18 x) pure returns (SD1x18 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > uint256(int256(uMAX_SD1x18))) {
revert CastingErrors.PRBMath_UD60x18_IntoSD1x18_Overflow(x);
}
result = SD1x18.wrap(int64(uint64(xUint)));
}
/// @notice Casts a UD60x18 number into UD2x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_UD2x18`.
function intoUD2x18(UD60x18 x) pure returns (UD2x18 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > uMAX_UD2x18) {
revert CastingErrors.PRBMath_UD60x18_IntoUD2x18_Overflow(x);
}
result = UD2x18.wrap(uint64(xUint));
}
/// @notice Casts a UD60x18 number into SD59x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_SD59x18`.
function intoSD59x18(UD60x18 x) pure returns (SD59x18 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > uint256(uMAX_SD59x18)) {
revert CastingErrors.PRBMath_UD60x18_IntoSD59x18_Overflow(x);
}
result = SD59x18.wrap(int256(xUint));
}
/// @notice Casts a UD60x18 number into uint128.
/// @dev This is basically an alias for {unwrap}.
function intoUint256(UD60x18 x) pure returns (uint256 result) {
result = UD60x18.unwrap(x);
}
/// @notice Casts a UD60x18 number into uint128.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT128`.
function intoUint128(UD60x18 x) pure returns (uint128 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > MAX_UINT128) {
revert CastingErrors.PRBMath_UD60x18_IntoUint128_Overflow(x);
}
result = uint128(xUint);
}
/// @notice Casts a UD60x18 number into uint40.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(UD60x18 x) pure returns (uint40 result) {
uint256 xUint = UD60x18.unwrap(x);
if (xUint > MAX_UINT40) {
revert CastingErrors.PRBMath_UD60x18_IntoUint40_Overflow(x);
}
result = uint40(xUint);
}
/// @notice Alias for {wrap}.
function ud(uint256 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(x);
}
/// @notice Alias for {wrap}.
function ud60x18(uint256 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(x);
}
/// @notice Unwraps a UD60x18 number into uint256.
function unwrap(UD60x18 x) pure returns (uint256 result) {
result = UD60x18.unwrap(x);
}
/// @notice Wraps a uint256 number into the UD60x18 value type.
function wrap(uint256 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(x);
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { uMAX_UD60x18, uUNIT } from "./Constants.sol";
import { PRBMath_UD60x18_Convert_Overflow } from "./Errors.sol";
import { UD60x18 } from "./ValueType.sol";
/// @notice Converts a UD60x18 number to a simple integer by dividing it by `UNIT`.
/// @dev The result is rounded toward zero.
/// @param x The UD60x18 number to convert.
/// @return result The same number in basic integer form.
function convert(UD60x18 x) pure returns (uint256 result) {
result = UD60x18.unwrap(x) / uUNIT;
}
/// @notice Converts a simple integer to UD60x18 by multiplying it by `UNIT`.
///
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UD60x18 / UNIT`.
///
/// @param x The basic integer to convert.
/// @param result The same number converted to UD60x18.
function convert(uint256 x) pure returns (UD60x18 result) {
if (x > uMAX_UD60x18 / uUNIT) {
revert PRBMath_UD60x18_Convert_Overflow(x);
}
unchecked {
result = UD60x18.wrap(x * uUNIT);
}
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD60x18 } from "./ValueType.sol";
// NOTICE: the "u" prefix stands for "unwrapped".
/// @dev Euler's number as a UD60x18 number.
UD60x18 constant E = UD60x18.wrap(2_718281828459045235);
/// @dev The maximum input permitted in {exp}.
uint256 constant uEXP_MAX_INPUT = 133_084258667509499440;
UD60x18 constant EXP_MAX_INPUT = UD60x18.wrap(uEXP_MAX_INPUT);
/// @dev The maximum input permitted in {exp2}.
uint256 constant uEXP2_MAX_INPUT = 192e18 - 1;
UD60x18 constant EXP2_MAX_INPUT = UD60x18.wrap(uEXP2_MAX_INPUT);
/// @dev Half the UNIT number.
uint256 constant uHALF_UNIT = 0.5e18;
UD60x18 constant HALF_UNIT = UD60x18.wrap(uHALF_UNIT);
/// @dev $log_2(10)$ as a UD60x18 number.
uint256 constant uLOG2_10 = 3_321928094887362347;
UD60x18 constant LOG2_10 = UD60x18.wrap(uLOG2_10);
/// @dev $log_2(e)$ as a UD60x18 number.
uint256 constant uLOG2_E = 1_442695040888963407;
UD60x18 constant LOG2_E = UD60x18.wrap(uLOG2_E);
/// @dev The maximum value a UD60x18 number can have.
uint256 constant uMAX_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_584007913129639935;
UD60x18 constant MAX_UD60x18 = UD60x18.wrap(uMAX_UD60x18);
/// @dev The maximum whole value a UD60x18 number can have.
uint256 constant uMAX_WHOLE_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_000000000000000000;
UD60x18 constant MAX_WHOLE_UD60x18 = UD60x18.wrap(uMAX_WHOLE_UD60x18);
/// @dev PI as a UD60x18 number.
UD60x18 constant PI = UD60x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of UD60x18.
uint256 constant uUNIT = 1e18;
UD60x18 constant UNIT = UD60x18.wrap(uUNIT);
/// @dev The unit number squared.
uint256 constant uUNIT_SQUARED = 1e36;
UD60x18 constant UNIT_SQUARED = UD60x18.wrap(uUNIT_SQUARED);
/// @dev Zero as a UD60x18 number.
UD60x18 constant ZERO = UD60x18.wrap(0);// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD60x18 } from "./ValueType.sol";
/// @notice Thrown when ceiling a number overflows UD60x18.
error PRBMath_UD60x18_Ceil_Overflow(UD60x18 x);
/// @notice Thrown when converting a basic integer to the fixed-point format overflows UD60x18.
error PRBMath_UD60x18_Convert_Overflow(uint256 x);
/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.
error PRBMath_UD60x18_Exp_InputTooBig(UD60x18 x);
/// @notice Thrown when taking the binary exponent of a base greater than 192e18.
error PRBMath_UD60x18_Exp2_InputTooBig(UD60x18 x);
/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows UD60x18.
error PRBMath_UD60x18_Gm_Overflow(UD60x18 x, UD60x18 y);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_UD60x18_IntoSD1x18_Overflow(UD60x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD59x18.
error PRBMath_UD60x18_IntoSD59x18_Overflow(UD60x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_UD60x18_IntoUD2x18_Overflow(UD60x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_UD60x18_IntoUint128_Overflow(UD60x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_UD60x18_IntoUint40_Overflow(UD60x18 x);
/// @notice Thrown when taking the logarithm of a number less than 1.
error PRBMath_UD60x18_Log_InputTooSmall(UD60x18 x);
/// @notice Thrown when calculating the square root overflows UD60x18.
error PRBMath_UD60x18_Sqrt_Overflow(UD60x18 x);// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { wrap } from "./Casting.sol";
import {
uEXP_MAX_INPUT,
uEXP2_MAX_INPUT,
uHALF_UNIT,
uLOG2_10,
uLOG2_E,
uMAX_UD60x18,
uMAX_WHOLE_UD60x18,
UNIT,
uUNIT,
uUNIT_SQUARED,
ZERO
} from "./Constants.sol";
import { UD60x18 } from "./ValueType.sol";
/*//////////////////////////////////////////////////////////////////////////
MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Calculates the arithmetic average of x and y using the following formula:
///
/// $$
/// avg(x, y) = (x & y) + ((xUint ^ yUint) / 2)
/// $$
///
/// In English, this is what this formula does:
///
/// 1. AND x and y.
/// 2. Calculate half of XOR x and y.
/// 3. Add the two results together.
///
/// This technique is known as SWAR, which stands for "SIMD within a register". You can read more about it here:
/// https://devblogs.microsoft.com/oldnewthing/20220207-00/?p=106223
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// @param x The first operand as a UD60x18 number.
/// @param y The second operand as a UD60x18 number.
/// @return result The arithmetic average as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function avg(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
uint256 yUint = y.unwrap();
unchecked {
result = wrap((xUint & yUint) + ((xUint ^ yUint) >> 1));
}
}
/// @notice Yields the smallest whole number greater than or equal to x.
///
/// @dev This is optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to `MAX_WHOLE_UD60x18`.
///
/// @param x The UD60x18 number to ceil.
/// @param result The smallest whole number greater than or equal to x, as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function ceil(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
if (xUint > uMAX_WHOLE_UD60x18) {
revert Errors.PRBMath_UD60x18_Ceil_Overflow(x);
}
assembly ("memory-safe") {
// Equivalent to `x % UNIT`.
let remainder := mod(x, uUNIT)
// Equivalent to `UNIT - remainder`.
let delta := sub(uUNIT, remainder)
// Equivalent to `x + remainder > 0 ? delta : 0`.
result := add(x, mul(delta, gt(remainder, 0)))
}
}
/// @notice Divides two UD60x18 numbers, returning a new UD60x18 number.
///
/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
///
/// @param x The numerator as a UD60x18 number.
/// @param y The denominator as a UD60x18 number.
/// @param result The quotient as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function div(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(Common.mulDiv(x.unwrap(), uUNIT, y.unwrap()));
}
/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Requirements:
/// - x must be less than 133_084258667509499441.
///
/// @param x The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
// This check prevents values greater than 192e18 from being passed to {exp2}.
if (xUint > uEXP_MAX_INPUT) {
revert Errors.PRBMath_UD60x18_Exp_InputTooBig(x);
}
unchecked {
// Inline the fixed-point multiplication to save gas.
uint256 doubleUnitProduct = xUint * uLOG2_E;
result = exp2(wrap(doubleUnitProduct / uUNIT));
}
}
/// @notice Calculates the binary exponent of x using the binary fraction method.
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693
///
/// Requirements:
/// - x must be less than 192e18.
/// - The result must fit in UD60x18.
///
/// @param x The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp2(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
// Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.
if (xUint > uEXP2_MAX_INPUT) {
revert Errors.PRBMath_UD60x18_Exp2_InputTooBig(x);
}
// Convert x to the 192.64-bit fixed-point format.
uint256 x_192x64 = (xUint << 64) / uUNIT;
// Pass x to the {Common.exp2} function, which uses the 192.64-bit fixed-point number representation.
result = wrap(Common.exp2(x_192x64));
}
/// @notice Yields the greatest whole number less than or equal to x.
/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
/// @param x The UD60x18 number to floor.
/// @param result The greatest whole number less than or equal to x, as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function floor(UD60x18 x) pure returns (UD60x18 result) {
assembly ("memory-safe") {
// Equivalent to `x % UNIT`.
let remainder := mod(x, uUNIT)
// Equivalent to `x - remainder > 0 ? remainder : 0)`.
result := sub(x, mul(remainder, gt(remainder, 0)))
}
}
/// @notice Yields the excess beyond the floor of x using the odd function definition.
/// @dev See https://en.wikipedia.org/wiki/Fractional_part.
/// @param x The UD60x18 number to get the fractional part of.
/// @param result The fractional part of x as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function frac(UD60x18 x) pure returns (UD60x18 result) {
assembly ("memory-safe") {
result := mod(x, uUNIT)
}
}
/// @notice Calculates the geometric mean of x and y, i.e. $\sqrt{x * y}$, rounding down.
///
/// @dev Requirements:
/// - x * y must fit in UD60x18.
///
/// @param x The first operand as a UD60x18 number.
/// @param y The second operand as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function gm(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
uint256 yUint = y.unwrap();
if (xUint == 0 || yUint == 0) {
return ZERO;
}
unchecked {
// Checking for overflow this way is faster than letting Solidity do it.
uint256 xyUint = xUint * yUint;
if (xyUint / xUint != yUint) {
revert Errors.PRBMath_UD60x18_Gm_Overflow(x, y);
}
// We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`
// during multiplication. See the comments in {Common.sqrt}.
result = wrap(Common.sqrt(xyUint));
}
}
/// @notice Calculates the inverse of x.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must not be zero.
///
/// @param x The UD60x18 number for which to calculate the inverse.
/// @return result The inverse as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function inv(UD60x18 x) pure returns (UD60x18 result) {
unchecked {
result = wrap(uUNIT_SQUARED / x.unwrap());
}
}
/// @notice Calculates the natural logarithm of x using the following formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The UD60x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function ln(UD60x18 x) pure returns (UD60x18 result) {
unchecked {
// Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that
// {log2} can return is ~196_205294292027477728.
result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);
}
}
/// @notice Calculates the common logarithm of x using the following formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// However, if x is an exact power of ten, a hard coded value is returned.
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The UD60x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function log10(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
if (xUint < uUNIT) {
revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);
}
// Note that the `mul` in this assembly block is the standard multiplication operation, not {UD60x18.mul}.
// prettier-ignore
assembly ("memory-safe") {
switch x
case 1 { result := mul(uUNIT, sub(0, 18)) }
case 10 { result := mul(uUNIT, sub(1, 18)) }
case 100 { result := mul(uUNIT, sub(2, 18)) }
case 1000 { result := mul(uUNIT, sub(3, 18)) }
case 10000 { result := mul(uUNIT, sub(4, 18)) }
case 100000 { result := mul(uUNIT, sub(5, 18)) }
case 1000000 { result := mul(uUNIT, sub(6, 18)) }
case 10000000 { result := mul(uUNIT, sub(7, 18)) }
case 100000000 { result := mul(uUNIT, sub(8, 18)) }
case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
case 1000000000000000000 { result := 0 }
case 10000000000000000000 { result := uUNIT }
case 100000000000000000000 { result := mul(uUNIT, 2) }
case 1000000000000000000000 { result := mul(uUNIT, 3) }
case 10000000000000000000000 { result := mul(uUNIT, 4) }
case 100000000000000000000000 { result := mul(uUNIT, 5) }
case 1000000000000000000000000 { result := mul(uUNIT, 6) }
case 10000000000000000000000000 { result := mul(uUNIT, 7) }
case 100000000000000000000000000 { result := mul(uUNIT, 8) }
case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 59) }
default { result := uMAX_UD60x18 }
}
if (result.unwrap() == uMAX_UD60x18) {
unchecked {
// Inline the fixed-point division to save gas.
result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);
}
}
}
/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:
///
/// $$
/// log_2{x} = n + log_2{y}, \text{ where } y = x*2^{-n}, \ y \in [1, 2)
/// $$
///
/// For $0 \leq x \lt 1$, the input is inverted:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x must be greater than zero.
///
/// @param x The UD60x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
if (xUint < uUNIT) {
revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);
}
unchecked {
// Calculate the integer part of the logarithm.
uint256 n = Common.msb(xUint / uUNIT);
// This is the integer part of the logarithm as a UD60x18 number. The operation can't overflow because n
// n is at most 255 and UNIT is 1e18.
uint256 resultUint = n * uUNIT;
// Calculate $y = x * 2^{-n}$.
uint256 y = xUint >> n;
// If y is the unit number, the fractional part is zero.
if (y == uUNIT) {
return wrap(resultUint);
}
// Calculate the fractional part via the iterative approximation.
// The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.
uint256 DOUBLE_UNIT = 2e18;
for (uint256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
y = (y * y) / uUNIT;
// Is y^2 >= 2e18 and so in the range [2e18, 4e18)?
if (y >= DOUBLE_UNIT) {
// Add the 2^{-m} factor to the logarithm.
resultUint += delta;
// Halve y, which corresponds to z/2 in the Wikipedia article.
y >>= 1;
}
}
result = wrap(resultUint);
}
}
/// @notice Multiplies two UD60x18 numbers together, returning a new UD60x18 number.
///
/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
///
/// @dev See the documentation in {Common.mulDiv18}.
/// @param x The multiplicand as a UD60x18 number.
/// @param y The multiplier as a UD60x18 number.
/// @return result The product as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function mul(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(Common.mulDiv18(x.unwrap(), y.unwrap()));
}
/// @notice Raises x to the power of y.
///
/// For $1 \leq x \leq \infty$, the following standard formula is used:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// For $0 \leq x \lt 1$, since the unsigned {log2} is undefined, an equivalent formula is used:
///
/// $$
/// i = \frac{1}{x}
/// w = 2^{log_2{i} * y}
/// x^y = \frac{1}{w}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2} and {mul}.
/// - Returns `UNIT` for 0^0.
/// - It may not perform well with very small values of x. Consider using SD59x18 as an alternative.
///
/// Requirements:
/// - Refer to the requirements in {exp2}, {log2}, and {mul}.
///
/// @param x The base as a UD60x18 number.
/// @param y The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function pow(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
uint256 yUint = y.unwrap();
// If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.
if (xUint == 0) {
return yUint == 0 ? UNIT : ZERO;
}
// If x is `UNIT`, the result is always `UNIT`.
else if (xUint == uUNIT) {
return UNIT;
}
// If y is zero, the result is always `UNIT`.
if (yUint == 0) {
return UNIT;
}
// If y is `UNIT`, the result is always x.
else if (yUint == uUNIT) {
return x;
}
// If x is greater than `UNIT`, use the standard formula.
if (xUint > uUNIT) {
result = exp2(mul(log2(x), y));
}
// Conversely, if x is less than `UNIT`, use the equivalent formula.
else {
UD60x18 i = wrap(uUNIT_SQUARED / xUint);
UD60x18 w = exp2(mul(log2(i), y));
result = wrap(uUNIT_SQUARED / w.unwrap());
}
}
/// @notice Raises x (a UD60x18 number) to the power y (an unsigned basic integer) using the well-known
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv18}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - The result must fit in UD60x18.
///
/// @param x The base as a UD60x18 number.
/// @param y The exponent as a uint256.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function powu(UD60x18 x, uint256 y) pure returns (UD60x18 result) {
// Calculate the first iteration of the loop in advance.
uint256 xUint = x.unwrap();
uint256 resultUint = y & 1 > 0 ? xUint : uUNIT;
// Equivalent to `for(y /= 2; y > 0; y /= 2)`.
for (y >>= 1; y > 0; y >>= 1) {
xUint = Common.mulDiv18(xUint, xUint);
// Equivalent to `y % 2 == 1`.
if (y & 1 > 0) {
resultUint = Common.mulDiv18(resultUint, xUint);
}
}
result = wrap(resultUint);
}
/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must be less than `MAX_UD60x18 / UNIT`.
///
/// @param x The UD60x18 number for which to calculate the square root.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function sqrt(UD60x18 x) pure returns (UD60x18 result) {
uint256 xUint = x.unwrap();
unchecked {
if (xUint > uMAX_UD60x18 / uUNIT) {
revert Errors.PRBMath_UD60x18_Sqrt_Overflow(x);
}
// Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two UD60x18 numbers.
// In this case, the two numbers are both the square root.
result = wrap(Common.sqrt(xUint * uUNIT));
}
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
import "./Helpers.sol" as Helpers;
import "./Math.sol" as Math;
/// @notice The unsigned 60.18-decimal fixed-point number representation, which can have up to 60 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the Solidity type uint256.
/// @dev The value type is defined here so it can be imported in all other files.
type UD60x18 is uint256;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoSD1x18,
Casting.intoUD2x18,
Casting.intoSD59x18,
Casting.intoUint128,
Casting.intoUint256,
Casting.intoUint40,
Casting.unwrap
} for UD60x18 global;
/*//////////////////////////////////////////////////////////////////////////
MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
// The global "using for" directive makes the functions in this library callable on the UD60x18 type.
using {
Math.avg,
Math.ceil,
Math.div,
Math.exp,
Math.exp2,
Math.floor,
Math.frac,
Math.gm,
Math.inv,
Math.ln,
Math.log10,
Math.log2,
Math.mul,
Math.pow,
Math.powu,
Math.sqrt
} for UD60x18 global;
/*//////////////////////////////////////////////////////////////////////////
HELPER FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
// The global "using for" directive makes the functions in this library callable on the UD60x18 type.
using {
Helpers.add,
Helpers.and,
Helpers.eq,
Helpers.gt,
Helpers.gte,
Helpers.isZero,
Helpers.lshift,
Helpers.lt,
Helpers.lte,
Helpers.mod,
Helpers.neq,
Helpers.not,
Helpers.or,
Helpers.rshift,
Helpers.sub,
Helpers.uncheckedAdd,
Helpers.uncheckedSub,
Helpers.xor
} for UD60x18 global;
/*//////////////////////////////////////////////////////////////////////////
OPERATORS
//////////////////////////////////////////////////////////////////////////*/
// The global "using for" directive makes it possible to use these operators on the UD60x18 type.
using {
Helpers.add as +,
Helpers.and2 as &,
Math.div as /,
Helpers.eq as ==,
Helpers.gt as >,
Helpers.gte as >=,
Helpers.lt as <,
Helpers.lte as <=,
Helpers.or as |,
Helpers.mod as %,
Math.mul as *,
Helpers.neq as !=,
Helpers.not as ~,
Helpers.sub as -,
Helpers.xor as ^
} for UD60x18 global;// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { wrap } from "./Casting.sol";
import { UD60x18 } from "./ValueType.sol";
/// @notice Implements the checked addition operation (+) in the UD60x18 type.
function add(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() + y.unwrap());
}
/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.
function and(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
result = wrap(x.unwrap() & bits);
}
/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.
function and2(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() & y.unwrap());
}
/// @notice Implements the equal operation (==) in the UD60x18 type.
function eq(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() == y.unwrap();
}
/// @notice Implements the greater than operation (>) in the UD60x18 type.
function gt(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() > y.unwrap();
}
/// @notice Implements the greater than or equal to operation (>=) in the UD60x18 type.
function gte(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() >= y.unwrap();
}
/// @notice Implements a zero comparison check function in the UD60x18 type.
function isZero(UD60x18 x) pure returns (bool result) {
// This wouldn't work if x could be negative.
result = x.unwrap() == 0;
}
/// @notice Implements the left shift operation (<<) in the UD60x18 type.
function lshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
result = wrap(x.unwrap() << bits);
}
/// @notice Implements the lower than operation (<) in the UD60x18 type.
function lt(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() < y.unwrap();
}
/// @notice Implements the lower than or equal to operation (<=) in the UD60x18 type.
function lte(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() <= y.unwrap();
}
/// @notice Implements the checked modulo operation (%) in the UD60x18 type.
function mod(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() % y.unwrap());
}
/// @notice Implements the not equal operation (!=) in the UD60x18 type.
function neq(UD60x18 x, UD60x18 y) pure returns (bool result) {
result = x.unwrap() != y.unwrap();
}
/// @notice Implements the NOT (~) bitwise operation in the UD60x18 type.
function not(UD60x18 x) pure returns (UD60x18 result) {
result = wrap(~x.unwrap());
}
/// @notice Implements the OR (|) bitwise operation in the UD60x18 type.
function or(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() | y.unwrap());
}
/// @notice Implements the right shift operation (>>) in the UD60x18 type.
function rshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
result = wrap(x.unwrap() >> bits);
}
/// @notice Implements the checked subtraction operation (-) in the UD60x18 type.
function sub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() - y.unwrap());
}
/// @notice Implements the unchecked addition operation (+) in the UD60x18 type.
function uncheckedAdd(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
unchecked {
result = wrap(x.unwrap() + y.unwrap());
}
}
/// @notice Implements the unchecked subtraction operation (-) in the UD60x18 type.
function uncheckedSub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
unchecked {
result = wrap(x.unwrap() - y.unwrap());
}
}
/// @notice Implements the XOR (^) bitwise operation in the UD60x18 type.
function xor(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
result = wrap(x.unwrap() ^ y.unwrap());
}// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/IERC165.sol)
pragma solidity ^0.8.20;
/**
* @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 >=0.8.19;
import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";
/// @notice Casts a UD2x18 number into SD1x18.
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(UD2x18 x) pure returns (SD1x18 result) {
uint64 xUint = UD2x18.unwrap(x);
if (xUint > uint64(uMAX_SD1x18)) {
revert Errors.PRBMath_UD2x18_IntoSD1x18_Overflow(x);
}
result = SD1x18.wrap(int64(xUint));
}
/// @notice Casts a UD2x18 number into SD59x18.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of SD59x18.
function intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));
}
/// @notice Casts a UD2x18 number into UD60x18.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of UD60x18.
function intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {
result = UD60x18.wrap(UD2x18.unwrap(x));
}
/// @notice Casts a UD2x18 number into uint128.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint128.
function intoUint128(UD2x18 x) pure returns (uint128 result) {
result = uint128(UD2x18.unwrap(x));
}
/// @notice Casts a UD2x18 number into uint256.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint256.
function intoUint256(UD2x18 x) pure returns (uint256 result) {
result = uint256(UD2x18.unwrap(x));
}
/// @notice Casts a UD2x18 number into uint40.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(UD2x18 x) pure returns (uint40 result) {
uint64 xUint = UD2x18.unwrap(x);
if (xUint > uint64(Common.MAX_UINT40)) {
revert Errors.PRBMath_UD2x18_IntoUint40_Overflow(x);
}
result = uint40(xUint);
}
/// @notice Alias for {wrap}.
function ud2x18(uint64 x) pure returns (UD2x18 result) {
result = UD2x18.wrap(x);
}
/// @notice Unwrap a UD2x18 number into uint64.
function unwrap(UD2x18 x) pure returns (uint64 result) {
result = UD2x18.unwrap(x);
}
/// @notice Wraps a uint64 number into UD2x18.
function wrap(uint64 x) pure returns (UD2x18 result) {
result = UD2x18.wrap(x);
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD2x18 } from "./ValueType.sol";
/// @dev Euler's number as a UD2x18 number.
UD2x18 constant E = UD2x18.wrap(2_718281828459045235);
/// @dev The maximum value a UD2x18 number can have.
uint64 constant uMAX_UD2x18 = 18_446744073709551615;
UD2x18 constant MAX_UD2x18 = UD2x18.wrap(uMAX_UD2x18);
/// @dev PI as a UD2x18 number.
UD2x18 constant PI = UD2x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of UD2x18.
UD2x18 constant UNIT = UD2x18.wrap(1e18);
uint64 constant uUNIT = 1e18;// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
/// @notice The unsigned 2.18-decimal fixed-point number representation, which can have up to 2 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type uint64. This is useful when end users want to use uint64 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD2x18 is uint64;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoSD1x18,
Casting.intoSD59x18,
Casting.intoUD60x18,
Casting.intoUint256,
Casting.intoUint128,
Casting.intoUint40,
Casting.unwrap
} for UD2x18 global;// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { UD2x18 } from "./ValueType.sol";
/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in SD1x18.
error PRBMath_UD2x18_IntoSD1x18_Overflow(UD2x18 x);
/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in uint40.
error PRBMath_UD2x18_IntoUint40_Overflow(UD2x18 x);// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
// Common.sol
//
// Common mathematical functions used in both SD59x18 and UD60x18. Note that these global functions do not
// always operate with SD59x18 and UD60x18 numbers.
/*//////////////////////////////////////////////////////////////////////////
CUSTOM ERRORS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Thrown when the resultant value in {mulDiv} overflows uint256.
error PRBMath_MulDiv_Overflow(uint256 x, uint256 y, uint256 denominator);
/// @notice Thrown when the resultant value in {mulDiv18} overflows uint256.
error PRBMath_MulDiv18_Overflow(uint256 x, uint256 y);
/// @notice Thrown when one of the inputs passed to {mulDivSigned} is `type(int256).min`.
error PRBMath_MulDivSigned_InputTooSmall();
/// @notice Thrown when the resultant value in {mulDivSigned} overflows int256.
error PRBMath_MulDivSigned_Overflow(int256 x, int256 y);
/*//////////////////////////////////////////////////////////////////////////
CONSTANTS
//////////////////////////////////////////////////////////////////////////*/
/// @dev The maximum value a uint128 number can have.
uint128 constant MAX_UINT128 = type(uint128).max;
/// @dev The maximum value a uint40 number can have.
uint40 constant MAX_UINT40 = type(uint40).max;
/// @dev The unit number, which the decimal precision of the fixed-point types.
uint256 constant UNIT = 1e18;
/// @dev The unit number inverted mod 2^256.
uint256 constant UNIT_INVERSE = 78156646155174841979727994598816262306175212592076161876661_508869554232690281;
/// @dev The the largest power of two that divides the decimal value of `UNIT`. The logarithm of this value is the least significant
/// bit in the binary representation of `UNIT`.
uint256 constant UNIT_LPOTD = 262144;
/*//////////////////////////////////////////////////////////////////////////
FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
/// @notice Calculates the binary exponent of x using the binary fraction method.
/// @dev Has to use 192.64-bit fixed-point numbers. See https://ethereum.stackexchange.com/a/96594/24693.
/// @param x The exponent as an unsigned 192.64-bit fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function exp2(uint256 x) pure returns (uint256 result) {
unchecked {
// Start from 0.5 in the 192.64-bit fixed-point format.
result = 0x800000000000000000000000000000000000000000000000;
// The following logic multiplies the result by $\sqrt{2^{-i}}$ when the bit at position i is 1. Key points:
//
// 1. Intermediate results will not overflow, as the starting point is 2^191 and all magic factors are under 2^65.
// 2. The rationale for organizing the if statements into groups of 8 is gas savings. If the result of performing
// a bitwise AND operation between x and any value in the array [0x80; 0x40; 0x20; 0x10; 0x08; 0x04; 0x02; 0x01] is 1,
// we know that `x & 0xFF` is also 1.
if (x & 0xFF00000000000000 > 0) {
if (x & 0x8000000000000000 > 0) {
result = (result * 0x16A09E667F3BCC909) >> 64;
}
if (x & 0x4000000000000000 > 0) {
result = (result * 0x1306FE0A31B7152DF) >> 64;
}
if (x & 0x2000000000000000 > 0) {
result = (result * 0x1172B83C7D517ADCE) >> 64;
}
if (x & 0x1000000000000000 > 0) {
result = (result * 0x10B5586CF9890F62A) >> 64;
}
if (x & 0x800000000000000 > 0) {
result = (result * 0x1059B0D31585743AE) >> 64;
}
if (x & 0x400000000000000 > 0) {
result = (result * 0x102C9A3E778060EE7) >> 64;
}
if (x & 0x200000000000000 > 0) {
result = (result * 0x10163DA9FB33356D8) >> 64;
}
if (x & 0x100000000000000 > 0) {
result = (result * 0x100B1AFA5ABCBED61) >> 64;
}
}
if (x & 0xFF000000000000 > 0) {
if (x & 0x80000000000000 > 0) {
result = (result * 0x10058C86DA1C09EA2) >> 64;
}
if (x & 0x40000000000000 > 0) {
result = (result * 0x1002C605E2E8CEC50) >> 64;
}
if (x & 0x20000000000000 > 0) {
result = (result * 0x100162F3904051FA1) >> 64;
}
if (x & 0x10000000000000 > 0) {
result = (result * 0x1000B175EFFDC76BA) >> 64;
}
if (x & 0x8000000000000 > 0) {
result = (result * 0x100058BA01FB9F96D) >> 64;
}
if (x & 0x4000000000000 > 0) {
result = (result * 0x10002C5CC37DA9492) >> 64;
}
if (x & 0x2000000000000 > 0) {
result = (result * 0x1000162E525EE0547) >> 64;
}
if (x & 0x1000000000000 > 0) {
result = (result * 0x10000B17255775C04) >> 64;
}
}
if (x & 0xFF0000000000 > 0) {
if (x & 0x800000000000 > 0) {
result = (result * 0x1000058B91B5BC9AE) >> 64;
}
if (x & 0x400000000000 > 0) {
result = (result * 0x100002C5C89D5EC6D) >> 64;
}
if (x & 0x200000000000 > 0) {
result = (result * 0x10000162E43F4F831) >> 64;
}
if (x & 0x100000000000 > 0) {
result = (result * 0x100000B1721BCFC9A) >> 64;
}
if (x & 0x80000000000 > 0) {
result = (result * 0x10000058B90CF1E6E) >> 64;
}
if (x & 0x40000000000 > 0) {
result = (result * 0x1000002C5C863B73F) >> 64;
}
if (x & 0x20000000000 > 0) {
result = (result * 0x100000162E430E5A2) >> 64;
}
if (x & 0x10000000000 > 0) {
result = (result * 0x1000000B172183551) >> 64;
}
}
if (x & 0xFF00000000 > 0) {
if (x & 0x8000000000 > 0) {
result = (result * 0x100000058B90C0B49) >> 64;
}
if (x & 0x4000000000 > 0) {
result = (result * 0x10000002C5C8601CC) >> 64;
}
if (x & 0x2000000000 > 0) {
result = (result * 0x1000000162E42FFF0) >> 64;
}
if (x & 0x1000000000 > 0) {
result = (result * 0x10000000B17217FBB) >> 64;
}
if (x & 0x800000000 > 0) {
result = (result * 0x1000000058B90BFCE) >> 64;
}
if (x & 0x400000000 > 0) {
result = (result * 0x100000002C5C85FE3) >> 64;
}
if (x & 0x200000000 > 0) {
result = (result * 0x10000000162E42FF1) >> 64;
}
if (x & 0x100000000 > 0) {
result = (result * 0x100000000B17217F8) >> 64;
}
}
if (x & 0xFF000000 > 0) {
if (x & 0x80000000 > 0) {
result = (result * 0x10000000058B90BFC) >> 64;
}
if (x & 0x40000000 > 0) {
result = (result * 0x1000000002C5C85FE) >> 64;
}
if (x & 0x20000000 > 0) {
result = (result * 0x100000000162E42FF) >> 64;
}
if (x & 0x10000000 > 0) {
result = (result * 0x1000000000B17217F) >> 64;
}
if (x & 0x8000000 > 0) {
result = (result * 0x100000000058B90C0) >> 64;
}
if (x & 0x4000000 > 0) {
result = (result * 0x10000000002C5C860) >> 64;
}
if (x & 0x2000000 > 0) {
result = (result * 0x1000000000162E430) >> 64;
}
if (x & 0x1000000 > 0) {
result = (result * 0x10000000000B17218) >> 64;
}
}
if (x & 0xFF0000 > 0) {
if (x & 0x800000 > 0) {
result = (result * 0x1000000000058B90C) >> 64;
}
if (x & 0x400000 > 0) {
result = (result * 0x100000000002C5C86) >> 64;
}
if (x & 0x200000 > 0) {
result = (result * 0x10000000000162E43) >> 64;
}
if (x & 0x100000 > 0) {
result = (result * 0x100000000000B1721) >> 64;
}
if (x & 0x80000 > 0) {
result = (result * 0x10000000000058B91) >> 64;
}
if (x & 0x40000 > 0) {
result = (result * 0x1000000000002C5C8) >> 64;
}
if (x & 0x20000 > 0) {
result = (result * 0x100000000000162E4) >> 64;
}
if (x & 0x10000 > 0) {
result = (result * 0x1000000000000B172) >> 64;
}
}
if (x & 0xFF00 > 0) {
if (x & 0x8000 > 0) {
result = (result * 0x100000000000058B9) >> 64;
}
if (x & 0x4000 > 0) {
result = (result * 0x10000000000002C5D) >> 64;
}
if (x & 0x2000 > 0) {
result = (result * 0x1000000000000162E) >> 64;
}
if (x & 0x1000 > 0) {
result = (result * 0x10000000000000B17) >> 64;
}
if (x & 0x800 > 0) {
result = (result * 0x1000000000000058C) >> 64;
}
if (x & 0x400 > 0) {
result = (result * 0x100000000000002C6) >> 64;
}
if (x & 0x200 > 0) {
result = (result * 0x10000000000000163) >> 64;
}
if (x & 0x100 > 0) {
result = (result * 0x100000000000000B1) >> 64;
}
}
if (x & 0xFF > 0) {
if (x & 0x80 > 0) {
result = (result * 0x10000000000000059) >> 64;
}
if (x & 0x40 > 0) {
result = (result * 0x1000000000000002C) >> 64;
}
if (x & 0x20 > 0) {
result = (result * 0x10000000000000016) >> 64;
}
if (x & 0x10 > 0) {
result = (result * 0x1000000000000000B) >> 64;
}
if (x & 0x8 > 0) {
result = (result * 0x10000000000000006) >> 64;
}
if (x & 0x4 > 0) {
result = (result * 0x10000000000000003) >> 64;
}
if (x & 0x2 > 0) {
result = (result * 0x10000000000000001) >> 64;
}
if (x & 0x1 > 0) {
result = (result * 0x10000000000000001) >> 64;
}
}
// In the code snippet below, two operations are executed simultaneously:
//
// 1. The result is multiplied by $(2^n + 1)$, where $2^n$ represents the integer part, and the additional 1
// accounts for the initial guess of 0.5. This is achieved by subtracting from 191 instead of 192.
// 2. The result is then converted to an unsigned 60.18-decimal fixed-point format.
//
// The underlying logic is based on the relationship $2^{191-ip} = 2^{ip} / 2^{191}$, where $ip$ denotes the,
// integer part, $2^n$.
result *= UNIT;
result >>= (191 - (x >> 64));
}
}
/// @notice Finds the zero-based index of the first 1 in the binary representation of x.
///
/// @dev See the note on "msb" in this Wikipedia article: https://en.wikipedia.org/wiki/Find_first_set
///
/// Each step in this implementation is equivalent to this high-level code:
///
/// ```solidity
/// if (x >= 2 ** 128) {
/// x >>= 128;
/// result += 128;
/// }
/// ```
///
/// Where 128 is replaced with each respective power of two factor. See the full high-level implementation here:
/// https://gist.github.com/PaulRBerg/f932f8693f2733e30c4d479e8e980948
///
/// The Yul instructions used below are:
///
/// - "gt" is "greater than"
/// - "or" is the OR bitwise operator
/// - "shl" is "shift left"
/// - "shr" is "shift right"
///
/// @param x The uint256 number for which to find the index of the most significant bit.
/// @return result The index of the most significant bit as a uint256.
/// @custom:smtchecker abstract-function-nondet
function msb(uint256 x) pure returns (uint256 result) {
// 2^128
assembly ("memory-safe") {
let factor := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^64
assembly ("memory-safe") {
let factor := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^32
assembly ("memory-safe") {
let factor := shl(5, gt(x, 0xFFFFFFFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^16
assembly ("memory-safe") {
let factor := shl(4, gt(x, 0xFFFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^8
assembly ("memory-safe") {
let factor := shl(3, gt(x, 0xFF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^4
assembly ("memory-safe") {
let factor := shl(2, gt(x, 0xF))
x := shr(factor, x)
result := or(result, factor)
}
// 2^2
assembly ("memory-safe") {
let factor := shl(1, gt(x, 0x3))
x := shr(factor, x)
result := or(result, factor)
}
// 2^1
// No need to shift x any more.
assembly ("memory-safe") {
let factor := gt(x, 0x1)
result := or(result, factor)
}
}
/// @notice Calculates x*y÷denominator with 512-bit precision.
///
/// @dev Credits to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - The denominator must not be zero.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as a uint256.
/// @param y The multiplier as a uint256.
/// @param denominator The divisor as a uint256.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function mulDiv(uint256 x, uint256 y, uint256 denominator) pure returns (uint256 result) {
// 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
// use the Chinese Remainder Theorem to reconstruct the 512-bit result. The result is stored in two 256
// variables such that product = prod1 * 2^256 + prod0.
uint256 prod0; // Least significant 256 bits of the product
uint256 prod1; // Most significant 256 bits of the product
assembly ("memory-safe") {
let mm := mulmod(x, y, not(0))
prod0 := mul(x, y)
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
// Handle non-overflow cases, 256 by 256 division.
if (prod1 == 0) {
unchecked {
return prod0 / denominator;
}
}
// Make sure the result is less than 2^256. Also prevents denominator == 0.
if (prod1 >= denominator) {
revert PRBMath_MulDiv_Overflow(x, y, denominator);
}
////////////////////////////////////////////////////////////////////////////
// 512 by 256 division
////////////////////////////////////////////////////////////////////////////
// Make division exact by subtracting the remainder from [prod1 prod0].
uint256 remainder;
assembly ("memory-safe") {
// Compute remainder using the mulmod Yul instruction.
remainder := mulmod(x, y, denominator)
// Subtract 256 bit number from 512-bit number.
prod1 := sub(prod1, gt(remainder, prod0))
prod0 := sub(prod0, remainder)
}
unchecked {
// Calculate the largest power of two divisor of the denominator using the unary operator ~. This operation cannot overflow
// because the denominator cannot be zero at this point in the function execution. The result is always >= 1.
// For more detail, see https://cs.stackexchange.com/q/138556/92363.
uint256 lpotdod = denominator & (~denominator + 1);
uint256 flippedLpotdod;
assembly ("memory-safe") {
// Factor powers of two out of denominator.
denominator := div(denominator, lpotdod)
// Divide [prod1 prod0] by lpotdod.
prod0 := div(prod0, lpotdod)
// Get the flipped value `2^256 / lpotdod`. If the `lpotdod` is zero, the flipped value is one.
// `sub(0, lpotdod)` produces the two's complement version of `lpotdod`, which is equivalent to flipping all the bits.
// However, `div` interprets this value as an unsigned value: https://ethereum.stackexchange.com/q/147168/24693
flippedLpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
}
// Shift in bits from prod1 into prod0.
prod0 |= prod1 * flippedLpotdod;
// Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
// that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
// four bits. That is, denominator * inv = 1 mod 2^4.
uint256 inverse = (3 * denominator) ^ 2;
// Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
// in modular arithmetic, doubling the correct bits in each step.
inverse *= 2 - denominator * inverse; // inverse mod 2^8
inverse *= 2 - denominator * inverse; // inverse mod 2^16
inverse *= 2 - denominator * inverse; // inverse mod 2^32
inverse *= 2 - denominator * inverse; // inverse mod 2^64
inverse *= 2 - denominator * inverse; // inverse mod 2^128
inverse *= 2 - denominator * inverse; // inverse mod 2^256
// Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
// This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
// less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
// is no longer required.
result = prod0 * inverse;
}
}
/// @notice Calculates x*y÷1e18 with 512-bit precision.
///
/// @dev A variant of {mulDiv} with constant folding, i.e. in which the denominator is hard coded to 1e18.
///
/// Notes:
/// - The body is purposely left uncommented; to understand how this works, see the documentation in {mulDiv}.
/// - The result is rounded toward zero.
/// - We take as an axiom that the result cannot be `MAX_UINT256` when x and y solve the following system of equations:
///
/// $$
/// \begin{cases}
/// x * y = MAX\_UINT256 * UNIT \\
/// (x * y) \% UNIT \geq \frac{UNIT}{2}
/// \end{cases}
/// $$
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function mulDiv18(uint256 x, uint256 y) pure returns (uint256 result) {
uint256 prod0;
uint256 prod1;
assembly ("memory-safe") {
let mm := mulmod(x, y, not(0))
prod0 := mul(x, y)
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
if (prod1 == 0) {
unchecked {
return prod0 / UNIT;
}
}
if (prod1 >= UNIT) {
revert PRBMath_MulDiv18_Overflow(x, y);
}
uint256 remainder;
assembly ("memory-safe") {
remainder := mulmod(x, y, UNIT)
result :=
mul(
or(
div(sub(prod0, remainder), UNIT_LPOTD),
mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, UNIT_LPOTD), UNIT_LPOTD), 1))
),
UNIT_INVERSE
)
}
}
/// @notice Calculates x*y÷denominator with 512-bit precision.
///
/// @dev This is an extension of {mulDiv} for signed numbers, which works by computing the signs and the absolute values separately.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - None of the inputs can be `type(int256).min`.
/// - The result must fit in int256.
///
/// @param x The multiplicand as an int256.
/// @param y The multiplier as an int256.
/// @param denominator The divisor as an int256.
/// @return result The result as an int256.
/// @custom:smtchecker abstract-function-nondet
function mulDivSigned(int256 x, int256 y, int256 denominator) pure returns (int256 result) {
if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
revert PRBMath_MulDivSigned_InputTooSmall();
}
// Get hold of the absolute values of x, y and the denominator.
uint256 xAbs;
uint256 yAbs;
uint256 dAbs;
unchecked {
xAbs = x < 0 ? uint256(-x) : uint256(x);
yAbs = y < 0 ? uint256(-y) : uint256(y);
dAbs = denominator < 0 ? uint256(-denominator) : uint256(denominator);
}
// Compute the absolute value of x*y÷denominator. The result must fit in int256.
uint256 resultAbs = mulDiv(xAbs, yAbs, dAbs);
if (resultAbs > uint256(type(int256).max)) {
revert PRBMath_MulDivSigned_Overflow(x, y);
}
// Get the signs of x, y and the denominator.
uint256 sx;
uint256 sy;
uint256 sd;
assembly ("memory-safe") {
// "sgt" is the "signed greater than" assembly instruction and "sub(0,1)" is -1 in two's complement.
sx := sgt(x, sub(0, 1))
sy := sgt(y, sub(0, 1))
sd := sgt(denominator, sub(0, 1))
}
// XOR over sx, sy and sd. What this does is to check whether there are 1 or 3 negative signs in the inputs.
// If there are, the result should be negative. Otherwise, it should be positive.
unchecked {
result = sx ^ sy ^ sd == 0 ? -int256(resultAbs) : int256(resultAbs);
}
}
/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - If x is not a perfect square, the result is rounded down.
/// - Credits to OpenZeppelin for the explanations in comments below.
///
/// @param x The uint256 number for which to calculate the square root.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function sqrt(uint256 x) pure returns (uint256 result) {
if (x == 0) {
return 0;
}
// For our first guess, we calculate the biggest power of 2 which is smaller than the square root of x.
//
// We know that the "msb" (most significant bit) of x is a power of 2 such that we have:
//
// $$
// msb(x) <= x <= 2*msb(x)$
// $$
//
// We write $msb(x)$ as $2^k$, and we get:
//
// $$
// k = log_2(x)
// $$
//
// Thus, we can write the initial inequality as:
//
// $$
// 2^{log_2(x)} <= x <= 2*2^{log_2(x)+1} \\
// sqrt(2^k) <= sqrt(x) < sqrt(2^{k+1}) \\
// 2^{k/2} <= sqrt(x) < 2^{(k+1)/2} <= 2^{(k/2)+1}
// $$
//
// Consequently, $2^{log_2(x) /2} is a good first approximation of sqrt(x) with at least one correct bit.
uint256 xAux = uint256(x);
result = 1;
if (xAux >= 2 ** 128) {
xAux >>= 128;
result <<= 64;
}
if (xAux >= 2 ** 64) {
xAux >>= 64;
result <<= 32;
}
if (xAux >= 2 ** 32) {
xAux >>= 32;
result <<= 16;
}
if (xAux >= 2 ** 16) {
xAux >>= 16;
result <<= 8;
}
if (xAux >= 2 ** 8) {
xAux >>= 8;
result <<= 4;
}
if (xAux >= 2 ** 4) {
xAux >>= 4;
result <<= 2;
}
if (xAux >= 2 ** 2) {
result <<= 1;
}
// At this point, `result` is an estimation with at least one bit of precision. We know the true value has at
// most 128 bits, since it is the square root of a uint256. Newton's method converges quadratically (precision
// doubles at every iteration). We thus need at most 7 iteration to turn our partial result with one bit of
// precision into the expected uint128 result.
unchecked {
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
// If x is not a perfect square, round the result toward zero.
uint256 roundedResult = x / result;
if (result >= roundedResult) {
result = roundedResult;
}
}
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
/// @notice The signed 1.18-decimal fixed-point number representation, which can have up to 1 digit and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int64. This is useful when end users want to use int64 to save gas, e.g. with tight variable packing in contract
/// storage.
type SD1x18 is int64;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoSD59x18,
Casting.intoUD2x18,
Casting.intoUD60x18,
Casting.intoUint256,
Casting.intoUint128,
Casting.intoUint40,
Casting.unwrap
} for SD1x18 global;// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD1x18 } from "./ValueType.sol";
/// @dev Euler's number as an SD1x18 number.
SD1x18 constant E = SD1x18.wrap(2_718281828459045235);
/// @dev The maximum value an SD1x18 number can have.
int64 constant uMAX_SD1x18 = 9_223372036854775807;
SD1x18 constant MAX_SD1x18 = SD1x18.wrap(uMAX_SD1x18);
/// @dev The maximum value an SD1x18 number can have.
int64 constant uMIN_SD1x18 = -9_223372036854775808;
SD1x18 constant MIN_SD1x18 = SD1x18.wrap(uMIN_SD1x18);
/// @dev PI as an SD1x18 number.
SD1x18 constant PI = SD1x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of SD1x18.
SD1x18 constant UNIT = SD1x18.wrap(1e18);
int64 constant uUNIT = 1e18;// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD59x18 } from "./ValueType.sol";
// NOTICE: the "u" prefix stands for "unwrapped".
/// @dev Euler's number as an SD59x18 number.
SD59x18 constant E = SD59x18.wrap(2_718281828459045235);
/// @dev The maximum input permitted in {exp}.
int256 constant uEXP_MAX_INPUT = 133_084258667509499440;
SD59x18 constant EXP_MAX_INPUT = SD59x18.wrap(uEXP_MAX_INPUT);
/// @dev Any value less than this returns 0 in {exp}.
int256 constant uEXP_MIN_THRESHOLD = -41_446531673892822322;
SD59x18 constant EXP_MIN_THRESHOLD = SD59x18.wrap(uEXP_MIN_THRESHOLD);
/// @dev The maximum input permitted in {exp2}.
int256 constant uEXP2_MAX_INPUT = 192e18 - 1;
SD59x18 constant EXP2_MAX_INPUT = SD59x18.wrap(uEXP2_MAX_INPUT);
/// @dev Any value less than this returns 0 in {exp2}.
int256 constant uEXP2_MIN_THRESHOLD = -59_794705707972522261;
SD59x18 constant EXP2_MIN_THRESHOLD = SD59x18.wrap(uEXP2_MIN_THRESHOLD);
/// @dev Half the UNIT number.
int256 constant uHALF_UNIT = 0.5e18;
SD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);
/// @dev $log_2(10)$ as an SD59x18 number.
int256 constant uLOG2_10 = 3_321928094887362347;
SD59x18 constant LOG2_10 = SD59x18.wrap(uLOG2_10);
/// @dev $log_2(e)$ as an SD59x18 number.
int256 constant uLOG2_E = 1_442695040888963407;
SD59x18 constant LOG2_E = SD59x18.wrap(uLOG2_E);
/// @dev The maximum value an SD59x18 number can have.
int256 constant uMAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_792003956564819967;
SD59x18 constant MAX_SD59x18 = SD59x18.wrap(uMAX_SD59x18);
/// @dev The maximum whole value an SD59x18 number can have.
int256 constant uMAX_WHOLE_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MAX_WHOLE_SD59x18 = SD59x18.wrap(uMAX_WHOLE_SD59x18);
/// @dev The minimum value an SD59x18 number can have.
int256 constant uMIN_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_792003956564819968;
SD59x18 constant MIN_SD59x18 = SD59x18.wrap(uMIN_SD59x18);
/// @dev The minimum whole value an SD59x18 number can have.
int256 constant uMIN_WHOLE_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MIN_WHOLE_SD59x18 = SD59x18.wrap(uMIN_WHOLE_SD59x18);
/// @dev PI as an SD59x18 number.
SD59x18 constant PI = SD59x18.wrap(3_141592653589793238);
/// @dev The unit number, which gives the decimal precision of SD59x18.
int256 constant uUNIT = 1e18;
SD59x18 constant UNIT = SD59x18.wrap(1e18);
/// @dev The unit number squared.
int256 constant uUNIT_SQUARED = 1e36;
SD59x18 constant UNIT_SQUARED = SD59x18.wrap(uUNIT_SQUARED);
/// @dev Zero as an SD59x18 number.
SD59x18 constant ZERO = SD59x18.wrap(0);// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Casting.sol" as Casting;
import "./Helpers.sol" as Helpers;
import "./Math.sol" as Math;
/// @notice The signed 59.18-decimal fixed-point number representation, which can have up to 59 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int256.
type SD59x18 is int256;
/*//////////////////////////////////////////////////////////////////////////
CASTING
//////////////////////////////////////////////////////////////////////////*/
using {
Casting.intoInt256,
Casting.intoSD1x18,
Casting.intoUD2x18,
Casting.intoUD60x18,
Casting.intoUint256,
Casting.intoUint128,
Casting.intoUint40,
Casting.unwrap
} for SD59x18 global;
/*//////////////////////////////////////////////////////////////////////////
MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
using {
Math.abs,
Math.avg,
Math.ceil,
Math.div,
Math.exp,
Math.exp2,
Math.floor,
Math.frac,
Math.gm,
Math.inv,
Math.log10,
Math.log2,
Math.ln,
Math.mul,
Math.pow,
Math.powu,
Math.sqrt
} for SD59x18 global;
/*//////////////////////////////////////////////////////////////////////////
HELPER FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/
using {
Helpers.add,
Helpers.and,
Helpers.eq,
Helpers.gt,
Helpers.gte,
Helpers.isZero,
Helpers.lshift,
Helpers.lt,
Helpers.lte,
Helpers.mod,
Helpers.neq,
Helpers.not,
Helpers.or,
Helpers.rshift,
Helpers.sub,
Helpers.uncheckedAdd,
Helpers.uncheckedSub,
Helpers.uncheckedUnary,
Helpers.xor
} for SD59x18 global;
/*//////////////////////////////////////////////////////////////////////////
OPERATORS
//////////////////////////////////////////////////////////////////////////*/
// The global "using for" directive makes it possible to use these operators on the SD59x18 type.
using {
Helpers.add as +,
Helpers.and2 as &,
Math.div as /,
Helpers.eq as ==,
Helpers.gt as >,
Helpers.gte as >=,
Helpers.lt as <,
Helpers.lte as <=,
Helpers.mod as %,
Math.mul as *,
Helpers.neq as !=,
Helpers.not as ~,
Helpers.or as |,
Helpers.sub as -,
Helpers.unary as -,
Helpers.xor as ^
} for SD59x18 global;// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD1x18 } from "./ValueType.sol";
/// @notice Casts an SD1x18 number into SD59x18.
/// @dev There is no overflow check because the domain of SD1x18 is a subset of SD59x18.
function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
}
/// @notice Casts an SD1x18 number into UD2x18.
/// - x must be positive.
function intoUD2x18(SD1x18 x) pure returns (UD2x18 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUD2x18_Underflow(x);
}
result = UD2x18.wrap(uint64(xInt));
}
/// @notice Casts an SD1x18 number into UD60x18.
/// @dev Requirements:
/// - x must be positive.
function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUD60x18_Underflow(x);
}
result = UD60x18.wrap(uint64(xInt));
}
/// @notice Casts an SD1x18 number into uint256.
/// @dev Requirements:
/// - x must be positive.
function intoUint256(SD1x18 x) pure returns (uint256 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);
}
result = uint256(uint64(xInt));
}
/// @notice Casts an SD1x18 number into uint128.
/// @dev Requirements:
/// - x must be positive.
function intoUint128(SD1x18 x) pure returns (uint128 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);
}
result = uint128(uint64(xInt));
}
/// @notice Casts an SD1x18 number into uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD1x18 x) pure returns (uint40 result) {
int64 xInt = SD1x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD1x18_ToUint40_Underflow(x);
}
if (xInt > int64(uint64(Common.MAX_UINT40))) {
revert CastingErrors.PRBMath_SD1x18_ToUint40_Overflow(x);
}
result = uint40(uint64(xInt));
}
/// @notice Alias for {wrap}.
function sd1x18(int64 x) pure returns (SD1x18 result) {
result = SD1x18.wrap(x);
}
/// @notice Unwraps an SD1x18 number into int64.
function unwrap(SD1x18 x) pure returns (int64 result) {
result = SD1x18.unwrap(x);
}
/// @notice Wraps an int64 number into SD1x18.
function wrap(int64 x) pure returns (SD1x18 result) {
result = SD1x18.wrap(x);
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "./Errors.sol" as CastingErrors;
import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18, uMIN_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD59x18 } from "./ValueType.sol";
/// @notice Casts an SD59x18 number into int256.
/// @dev This is basically a functional alias for {unwrap}.
function intoInt256(SD59x18 x) pure returns (int256 result) {
result = SD59x18.unwrap(x);
}
/// @notice Casts an SD59x18 number into SD1x18.
/// @dev Requirements:
/// - x must be greater than or equal to `uMIN_SD1x18`.
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < uMIN_SD1x18) {
revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Underflow(x);
}
if (xInt > uMAX_SD1x18) {
revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Overflow(x);
}
result = SD1x18.wrap(int64(xInt));
}
/// @notice Casts an SD59x18 number into UD2x18.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `uMAX_UD2x18`.
function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Underflow(x);
}
if (xInt > int256(uint256(uMAX_UD2x18))) {
revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Overflow(x);
}
result = UD2x18.wrap(uint64(uint256(xInt)));
}
/// @notice Casts an SD59x18 number into UD60x18.
/// @dev Requirements:
/// - x must be positive.
function intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUD60x18_Underflow(x);
}
result = UD60x18.wrap(uint256(xInt));
}
/// @notice Casts an SD59x18 number into uint256.
/// @dev Requirements:
/// - x must be positive.
function intoUint256(SD59x18 x) pure returns (uint256 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUint256_Underflow(x);
}
result = uint256(xInt);
}
/// @notice Casts an SD59x18 number into uint128.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `uMAX_UINT128`.
function intoUint128(SD59x18 x) pure returns (uint128 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUint128_Underflow(x);
}
if (xInt > int256(uint256(MAX_UINT128))) {
revert CastingErrors.PRBMath_SD59x18_IntoUint128_Overflow(x);
}
result = uint128(uint256(xInt));
}
/// @notice Casts an SD59x18 number into uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD59x18 x) pure returns (uint40 result) {
int256 xInt = SD59x18.unwrap(x);
if (xInt < 0) {
revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);
}
if (xInt > int256(uint256(MAX_UINT40))) {
revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);
}
result = uint40(uint256(xInt));
}
/// @notice Alias for {wrap}.
function sd(int256 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(x);
}
/// @notice Alias for {wrap}.
function sd59x18(int256 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(x);
}
/// @notice Unwraps an SD59x18 number into int256.
function unwrap(SD59x18 x) pure returns (int256 result) {
result = SD59x18.unwrap(x);
}
/// @notice Wraps an int256 number into SD59x18.
function wrap(int256 x) pure returns (SD59x18 result) {
result = SD59x18.wrap(x);
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { wrap } from "./Casting.sol";
import { SD59x18 } from "./ValueType.sol";
/// @notice Implements the checked addition operation (+) in the SD59x18 type.
function add(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
return wrap(x.unwrap() + y.unwrap());
}
/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and(SD59x18 x, int256 bits) pure returns (SD59x18 result) {
return wrap(x.unwrap() & bits);
}
/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and2(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
return wrap(x.unwrap() & y.unwrap());
}
/// @notice Implements the equal (=) operation in the SD59x18 type.
function eq(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() == y.unwrap();
}
/// @notice Implements the greater than operation (>) in the SD59x18 type.
function gt(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() > y.unwrap();
}
/// @notice Implements the greater than or equal to operation (>=) in the SD59x18 type.
function gte(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() >= y.unwrap();
}
/// @notice Implements a zero comparison check function in the SD59x18 type.
function isZero(SD59x18 x) pure returns (bool result) {
result = x.unwrap() == 0;
}
/// @notice Implements the left shift operation (<<) in the SD59x18 type.
function lshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
result = wrap(x.unwrap() << bits);
}
/// @notice Implements the lower than operation (<) in the SD59x18 type.
function lt(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() < y.unwrap();
}
/// @notice Implements the lower than or equal to operation (<=) in the SD59x18 type.
function lte(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() <= y.unwrap();
}
/// @notice Implements the unchecked modulo operation (%) in the SD59x18 type.
function mod(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
result = wrap(x.unwrap() % y.unwrap());
}
/// @notice Implements the not equal operation (!=) in the SD59x18 type.
function neq(SD59x18 x, SD59x18 y) pure returns (bool result) {
result = x.unwrap() != y.unwrap();
}
/// @notice Implements the NOT (~) bitwise operation in the SD59x18 type.
function not(SD59x18 x) pure returns (SD59x18 result) {
result = wrap(~x.unwrap());
}
/// @notice Implements the OR (|) bitwise operation in the SD59x18 type.
function or(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
result = wrap(x.unwrap() | y.unwrap());
}
/// @notice Implements the right shift operation (>>) in the SD59x18 type.
function rshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
result = wrap(x.unwrap() >> bits);
}
/// @notice Implements the checked subtraction operation (-) in the SD59x18 type.
function sub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
result = wrap(x.unwrap() - y.unwrap());
}
/// @notice Implements the checked unary minus operation (-) in the SD59x18 type.
function unary(SD59x18 x) pure returns (SD59x18 result) {
result = wrap(-x.unwrap());
}
/// @notice Implements the unchecked addition operation (+) in the SD59x18 type.
function uncheckedAdd(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
unchecked {
result = wrap(x.unwrap() + y.unwrap());
}
}
/// @notice Implements the unchecked subtraction operation (-) in the SD59x18 type.
function uncheckedSub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
unchecked {
result = wrap(x.unwrap() - y.unwrap());
}
}
/// @notice Implements the unchecked unary minus operation (-) in the SD59x18 type.
function uncheckedUnary(SD59x18 x) pure returns (SD59x18 result) {
unchecked {
result = wrap(-x.unwrap());
}
}
/// @notice Implements the XOR (^) bitwise operation in the SD59x18 type.
function xor(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
result = wrap(x.unwrap() ^ y.unwrap());
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import {
uEXP_MAX_INPUT,
uEXP2_MAX_INPUT,
uEXP_MIN_THRESHOLD,
uEXP2_MIN_THRESHOLD,
uHALF_UNIT,
uLOG2_10,
uLOG2_E,
uMAX_SD59x18,
uMAX_WHOLE_SD59x18,
uMIN_SD59x18,
uMIN_WHOLE_SD59x18,
UNIT,
uUNIT,
uUNIT_SQUARED,
ZERO
} from "./Constants.sol";
import { wrap } from "./Helpers.sol";
import { SD59x18 } from "./ValueType.sol";
/// @notice Calculates the absolute value of x.
///
/// @dev Requirements:
/// - x must be greater than `MIN_SD59x18`.
///
/// @param x The SD59x18 number for which to calculate the absolute value.
/// @param result The absolute value of x as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function abs(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt == uMIN_SD59x18) {
revert Errors.PRBMath_SD59x18_Abs_MinSD59x18();
}
result = xInt < 0 ? wrap(-xInt) : x;
}
/// @notice Calculates the arithmetic average of x and y.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The arithmetic average as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
unchecked {
// This operation is equivalent to `x / 2 + y / 2`, and it can never overflow.
int256 sum = (xInt >> 1) + (yInt >> 1);
if (sum < 0) {
// If at least one of x and y is odd, add 1 to the result, because shifting negative numbers to the right
// rounds toward negative infinity. The right part is equivalent to `sum + (x % 2 == 1 || y % 2 == 1)`.
assembly ("memory-safe") {
result := add(sum, and(or(xInt, yInt), 1))
}
} else {
// Add 1 if both x and y are odd to account for the double 0.5 remainder truncated after shifting.
result = wrap(sum + (xInt & yInt & 1));
}
}
}
/// @notice Yields the smallest whole number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to `MAX_WHOLE_SD59x18`.
///
/// @param x The SD59x18 number to ceil.
/// @param result The smallest whole number greater than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ceil(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt > uMAX_WHOLE_SD59x18) {
revert Errors.PRBMath_SD59x18_Ceil_Overflow(x);
}
int256 remainder = xInt % uUNIT;
if (remainder == 0) {
result = x;
} else {
unchecked {
// Solidity uses C fmod style, which returns a modulus with the same sign as x.
int256 resultInt = xInt - remainder;
if (xInt > 0) {
resultInt += uUNIT;
}
result = wrap(resultInt);
}
}
}
/// @notice Divides two SD59x18 numbers, returning a new SD59x18 number.
///
/// @dev This is an extension of {Common.mulDiv} for signed numbers, which works by computing the signs and the absolute
/// values separately.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The denominator must not be zero.
/// - The result must fit in SD59x18.
///
/// @param x The numerator as an SD59x18 number.
/// @param y The denominator as an SD59x18 number.
/// @param result The quotient as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
revert Errors.PRBMath_SD59x18_Div_InputTooSmall();
}
// Get hold of the absolute values of x and y.
uint256 xAbs;
uint256 yAbs;
unchecked {
xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);
yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);
}
// Compute the absolute value (x*UNIT÷y). The resulting value must fit in SD59x18.
uint256 resultAbs = Common.mulDiv(xAbs, uint256(uUNIT), yAbs);
if (resultAbs > uint256(uMAX_SD59x18)) {
revert Errors.PRBMath_SD59x18_Div_Overflow(x, y);
}
// Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
// negative, 0 for positive or zero).
bool sameSign = (xInt ^ yInt) > -1;
// If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
unchecked {
result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
}
}
/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}.
///
/// Requirements:
/// - Refer to the requirements in {exp2}.
/// - x must be less than 133_084258667509499441.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
// Any input less than the threshold returns zero.
// This check also prevents an overflow for very small numbers.
if (xInt < uEXP_MIN_THRESHOLD) {
return ZERO;
}
// This check prevents values greater than 192e18 from being passed to {exp2}.
if (xInt > uEXP_MAX_INPUT) {
revert Errors.PRBMath_SD59x18_Exp_InputTooBig(x);
}
unchecked {
// Inline the fixed-point multiplication to save gas.
int256 doubleUnitProduct = xInt * uLOG2_E;
result = exp2(wrap(doubleUnitProduct / uUNIT));
}
}
/// @notice Calculates the binary exponent of x using the binary fraction method using the following formula:
///
/// $$
/// 2^{-x} = \frac{1}{2^x}
/// $$
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Notes:
/// - If x is less than -59_794705707972522261, the result is zero.
///
/// Requirements:
/// - x must be less than 192e18.
/// - The result must fit in SD59x18.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp2(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt < 0) {
// The inverse of any number less than the threshold is truncated to zero.
if (xInt < uEXP2_MIN_THRESHOLD) {
return ZERO;
}
unchecked {
// Inline the fixed-point inversion to save gas.
result = wrap(uUNIT_SQUARED / exp2(wrap(-xInt)).unwrap());
}
} else {
// Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.
if (xInt > uEXP2_MAX_INPUT) {
revert Errors.PRBMath_SD59x18_Exp2_InputTooBig(x);
}
unchecked {
// Convert x to the 192.64-bit fixed-point format.
uint256 x_192x64 = uint256((xInt << 64) / uUNIT);
// It is safe to cast the result to int256 due to the checks above.
result = wrap(int256(Common.exp2(x_192x64)));
}
}
}
/// @notice Yields the greatest whole number less than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be greater than or equal to `MIN_WHOLE_SD59x18`.
///
/// @param x The SD59x18 number to floor.
/// @param result The greatest whole number less than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function floor(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt < uMIN_WHOLE_SD59x18) {
revert Errors.PRBMath_SD59x18_Floor_Underflow(x);
}
int256 remainder = xInt % uUNIT;
if (remainder == 0) {
result = x;
} else {
unchecked {
// Solidity uses C fmod style, which returns a modulus with the same sign as x.
int256 resultInt = xInt - remainder;
if (xInt < 0) {
resultInt -= uUNIT;
}
result = wrap(resultInt);
}
}
}
/// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right.
/// of the radix point for negative numbers.
/// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
/// @param x The SD59x18 number to get the fractional part of.
/// @param result The fractional part of x as an SD59x18 number.
function frac(SD59x18 x) pure returns (SD59x18 result) {
result = wrap(x.unwrap() % uUNIT);
}
/// @notice Calculates the geometric mean of x and y, i.e. $\sqrt{x * y}$.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x * y must fit in SD59x18.
/// - x * y must not be negative, since complex numbers are not supported.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function gm(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
if (xInt == 0 || yInt == 0) {
return ZERO;
}
unchecked {
// Equivalent to `xy / x != y`. Checking for overflow this way is faster than letting Solidity do it.
int256 xyInt = xInt * yInt;
if (xyInt / xInt != yInt) {
revert Errors.PRBMath_SD59x18_Gm_Overflow(x, y);
}
// The product must not be negative, since complex numbers are not supported.
if (xyInt < 0) {
revert Errors.PRBMath_SD59x18_Gm_NegativeProduct(x, y);
}
// We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`
// during multiplication. See the comments in {Common.sqrt}.
uint256 resultUint = Common.sqrt(uint256(xyInt));
result = wrap(int256(resultUint));
}
}
/// @notice Calculates the inverse of x.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must not be zero.
///
/// @param x The SD59x18 number for which to calculate the inverse.
/// @return result The inverse as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function inv(SD59x18 x) pure returns (SD59x18 result) {
result = wrap(uUNIT_SQUARED / x.unwrap());
}
/// @notice Calculates the natural logarithm of x using the following formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ln(SD59x18 x) pure returns (SD59x18 result) {
// Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that
// {log2} can return is ~195_205294292027477728.
result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);
}
/// @notice Calculates the common logarithm of x using the following formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// However, if x is an exact power of ten, a hard coded value is returned.
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log10(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt < 0) {
revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
}
// Note that the `mul` in this block is the standard multiplication operation, not {SD59x18.mul}.
// prettier-ignore
assembly ("memory-safe") {
switch x
case 1 { result := mul(uUNIT, sub(0, 18)) }
case 10 { result := mul(uUNIT, sub(1, 18)) }
case 100 { result := mul(uUNIT, sub(2, 18)) }
case 1000 { result := mul(uUNIT, sub(3, 18)) }
case 10000 { result := mul(uUNIT, sub(4, 18)) }
case 100000 { result := mul(uUNIT, sub(5, 18)) }
case 1000000 { result := mul(uUNIT, sub(6, 18)) }
case 10000000 { result := mul(uUNIT, sub(7, 18)) }
case 100000000 { result := mul(uUNIT, sub(8, 18)) }
case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
case 1000000000000000000 { result := 0 }
case 10000000000000000000 { result := uUNIT }
case 100000000000000000000 { result := mul(uUNIT, 2) }
case 1000000000000000000000 { result := mul(uUNIT, 3) }
case 10000000000000000000000 { result := mul(uUNIT, 4) }
case 100000000000000000000000 { result := mul(uUNIT, 5) }
case 1000000000000000000000000 { result := mul(uUNIT, 6) }
case 10000000000000000000000000 { result := mul(uUNIT, 7) }
case 100000000000000000000000000 { result := mul(uUNIT, 8) }
case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
default { result := uMAX_SD59x18 }
}
if (result.unwrap() == uMAX_SD59x18) {
unchecked {
// Inline the fixed-point division to save gas.
result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);
}
}
}
/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:
///
/// $$
/// log_2{x} = n + log_2{y}, \text{ where } y = x*2^{-n}, \ y \in [1, 2)
/// $$
///
/// For $0 \leq x \lt 1$, the input is inverted:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation.
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x must be greater than zero.
///
/// @param x The SD59x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt <= 0) {
revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
}
unchecked {
int256 sign;
if (xInt >= uUNIT) {
sign = 1;
} else {
sign = -1;
// Inline the fixed-point inversion to save gas.
xInt = uUNIT_SQUARED / xInt;
}
// Calculate the integer part of the logarithm.
uint256 n = Common.msb(uint256(xInt / uUNIT));
// This is the integer part of the logarithm as an SD59x18 number. The operation can't overflow
// because n is at most 255, `UNIT` is 1e18, and the sign is either 1 or -1.
int256 resultInt = int256(n) * uUNIT;
// Calculate $y = x * 2^{-n}$.
int256 y = xInt >> n;
// If y is the unit number, the fractional part is zero.
if (y == uUNIT) {
return wrap(resultInt * sign);
}
// Calculate the fractional part via the iterative approximation.
// The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.
int256 DOUBLE_UNIT = 2e18;
for (int256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
y = (y * y) / uUNIT;
// Is y^2 >= 2e18 and so in the range [2e18, 4e18)?
if (y >= DOUBLE_UNIT) {
// Add the 2^{-m} factor to the logarithm.
resultInt = resultInt + delta;
// Halve y, which corresponds to z/2 in the Wikipedia article.
y >>= 1;
}
}
resultInt *= sign;
result = wrap(resultInt);
}
}
/// @notice Multiplies two SD59x18 numbers together, returning a new SD59x18 number.
///
/// @dev Notes:
/// - Refer to the notes in {Common.mulDiv18}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv18}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The result must fit in SD59x18.
///
/// @param x The multiplicand as an SD59x18 number.
/// @param y The multiplier as an SD59x18 number.
/// @return result The product as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function mul(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
revert Errors.PRBMath_SD59x18_Mul_InputTooSmall();
}
// Get hold of the absolute values of x and y.
uint256 xAbs;
uint256 yAbs;
unchecked {
xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);
yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);
}
// Compute the absolute value (x*y÷UNIT). The resulting value must fit in SD59x18.
uint256 resultAbs = Common.mulDiv18(xAbs, yAbs);
if (resultAbs > uint256(uMAX_SD59x18)) {
revert Errors.PRBMath_SD59x18_Mul_Overflow(x, y);
}
// Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
// negative, 0 for positive or zero).
bool sameSign = (xInt ^ yInt) > -1;
// If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
unchecked {
result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
}
}
/// @notice Raises x to the power of y using the following formula:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}, {log2}, and {mul}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {exp2}, {log2}, and {mul}.
///
/// @param x The base as an SD59x18 number.
/// @param y Exponent to raise x to, as an SD59x18 number
/// @return result x raised to power y, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function pow(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
int256 yInt = y.unwrap();
// If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.
if (xInt == 0) {
return yInt == 0 ? UNIT : ZERO;
}
// If x is `UNIT`, the result is always `UNIT`.
else if (xInt == uUNIT) {
return UNIT;
}
// If y is zero, the result is always `UNIT`.
if (yInt == 0) {
return UNIT;
}
// If y is `UNIT`, the result is always x.
else if (yInt == uUNIT) {
return x;
}
// Calculate the result using the formula.
result = exp2(mul(log2(x), y));
}
/// @notice Raises x (an SD59x18 number) to the power y (an unsigned basic integer) using the well-known
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv18}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {abs} and {Common.mulDiv18}.
/// - The result must fit in SD59x18.
///
/// @param x The base as an SD59x18 number.
/// @param y The exponent as a uint256.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {
uint256 xAbs = uint256(abs(x).unwrap());
// Calculate the first iteration of the loop in advance.
uint256 resultAbs = y & 1 > 0 ? xAbs : uint256(uUNIT);
// Equivalent to `for(y /= 2; y > 0; y /= 2)`.
uint256 yAux = y;
for (yAux >>= 1; yAux > 0; yAux >>= 1) {
xAbs = Common.mulDiv18(xAbs, xAbs);
// Equivalent to `y % 2 == 1`.
if (yAux & 1 > 0) {
resultAbs = Common.mulDiv18(resultAbs, xAbs);
}
}
// The result must fit in SD59x18.
if (resultAbs > uint256(uMAX_SD59x18)) {
revert Errors.PRBMath_SD59x18_Powu_Overflow(x, y);
}
unchecked {
// Is the base negative and the exponent odd? If yes, the result should be negative.
int256 resultInt = int256(resultAbs);
bool isNegative = x.unwrap() < 0 && y & 1 == 1;
if (isNegative) {
resultInt = -resultInt;
}
result = wrap(resultInt);
}
}
/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - Only the positive root is returned.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x cannot be negative, since complex numbers are not supported.
/// - x must be less than `MAX_SD59x18 / UNIT`.
///
/// @param x The SD59x18 number for which to calculate the square root.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function sqrt(SD59x18 x) pure returns (SD59x18 result) {
int256 xInt = x.unwrap();
if (xInt < 0) {
revert Errors.PRBMath_SD59x18_Sqrt_NegativeInput(x);
}
if (xInt > uMAX_SD59x18 / uUNIT) {
revert Errors.PRBMath_SD59x18_Sqrt_Overflow(x);
}
unchecked {
// Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two SD59x18 numbers.
// In this case, the two numbers are both the square root.
uint256 resultUint = Common.sqrt(uint256(xInt * uUNIT));
result = wrap(int256(resultUint));
}
}// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD1x18 } from "./ValueType.sol";
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD2x18.
error PRBMath_SD1x18_ToUD2x18_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD60x18.
error PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint128.
error PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint256.
error PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);
/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;
import { SD59x18 } from "./ValueType.sol";
/// @notice Thrown when taking the absolute value of `MIN_SD59x18`.
error PRBMath_SD59x18_Abs_MinSD59x18();
/// @notice Thrown when ceiling a number overflows SD59x18.
error PRBMath_SD59x18_Ceil_Overflow(SD59x18 x);
/// @notice Thrown when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMath_SD59x18_Convert_Overflow(int256 x);
/// @notice Thrown when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMath_SD59x18_Convert_Underflow(int256 x);
/// @notice Thrown when dividing two numbers and one of them is `MIN_SD59x18`.
error PRBMath_SD59x18_Div_InputTooSmall();
/// @notice Thrown when dividing two numbers and one of the intermediary unsigned results overflows SD59x18.
error PRBMath_SD59x18_Div_Overflow(SD59x18 x, SD59x18 y);
/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.
error PRBMath_SD59x18_Exp_InputTooBig(SD59x18 x);
/// @notice Thrown when taking the binary exponent of a base greater than 192e18.
error PRBMath_SD59x18_Exp2_InputTooBig(SD59x18 x);
/// @notice Thrown when flooring a number underflows SD59x18.
error PRBMath_SD59x18_Floor_Underflow(SD59x18 x);
/// @notice Thrown when taking the geometric mean of two numbers and their product is negative.
error PRBMath_SD59x18_Gm_NegativeProduct(SD59x18 x, SD59x18 y);
/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows SD59x18.
error PRBMath_SD59x18_Gm_Overflow(SD59x18 x, SD59x18 y);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD60x18.
error PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint256.
error PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);
/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);
/// @notice Thrown when taking the logarithm of a number less than or equal to zero.
error PRBMath_SD59x18_Log_InputTooSmall(SD59x18 x);
/// @notice Thrown when multiplying two numbers and one of the inputs is `MIN_SD59x18`.
error PRBMath_SD59x18_Mul_InputTooSmall();
/// @notice Thrown when multiplying two numbers and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Mul_Overflow(SD59x18 x, SD59x18 y);
/// @notice Thrown when raising a number to a power and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);
/// @notice Thrown when taking the square root of a negative number.
error PRBMath_SD59x18_Sqrt_NegativeInput(SD59x18 x);
/// @notice Thrown when the calculating the square root overflows SD59x18.
error PRBMath_SD59x18_Sqrt_Overflow(SD59x18 x);{
"optimizer": {
"enabled": true,
"mode": "z",
"fallback_to_optimizing_for_size": true
},
"viaIR": true,
"evmVersion": "paris",
"outputSelection": {
"*": {
"*": [
"abi"
]
}
},
"detectMissingLibraries": false,
"forceEVMLA": false,
"enableEraVMExtensions": false,
"libraries": {}
}Contract Security Audit
- No Contract Security Audit Submitted- Submit Audit Here
[{"inputs":[{"internalType":"contract IERC721Metadata","name":"nft","type":"address"},{"internalType":"string","name":"symbol","type":"string"}],"name":"SablierV2NFTDescriptor_UnknownNFT","type":"error"},{"inputs":[{"internalType":"uint256","name":"value","type":"uint256"},{"internalType":"uint256","name":"length","type":"uint256"}],"name":"StringsInsufficientHexLength","type":"error"},{"inputs":[{"internalType":"contract IERC721Metadata","name":"sablier","type":"address"},{"internalType":"uint256","name":"streamId","type":"uint256"}],"name":"tokenURI","outputs":[{"internalType":"string","name":"uri","type":"string"}],"stateMutability":"view","type":"function"}]Contract Creation Code
9c4d535b00000000000000000000000000000000000000000000000000000000000000000100070d08e54561dd015b5431d289d5e05a0d50e411d5e485e1d3a9536a2ec800000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000
Deployed Bytecode
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Multichain Portfolio | 30 Chains
| Chain | Token | Portfolio % | Price | Amount | Value |
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A contract address hosts a smart contract, which is a set of code stored on the blockchain that runs when predetermined conditions are met. Learn more about addresses in our Knowledge Base.