LinFormula

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This contract provides functions for calculating the purchase and sale return values on a linear curve using a scaling factor. The formula converts a given reserve token amount into a token return and the sale of a token amount into a reserve token return.

State Variables

OPTIMAL_TERM_MAX_VAL

Value that represents the point at which the optimal function approximations are still effective

uint8 private constant OPTIMAL_TERM_MAX_VAL = 0x6a;

MAX_SCALE

Max scaling factor in parts per million

uint32 private constant MAX_SCALE = 100000000;

PURE_LINEAR_SCALE

1:1 scaling factor in parts per million

uint32 private constant PURE_LINEAR_SCALE = 1000000;

WAD

Wei as decimal precision for calculations

uint256 private constant WAD = 10 ** 18;

Functions

_calculateLinPurchaseReturn

Returns the purchase value for a given amount (in the reserve token) as a conversion into the main token.

function _calculateLinPurchaseReturn(
    uint256 supply,
    uint256 reserveBalance,
    uint256 initialCost,
    uint32 scalingFactor,
    uint256 depositAmount
) internal pure returns (uint256 purchaseReturn);

Parameters

Name	Type	Description
supply	uint256	token total supply
reserveBalance	uint256	balance of the reserve token
initialCost	uint256	initial cost of the token
scalingFactor	uint32	scaling factor, represented in ppm, 1-1000000
depositAmount	uint256	deposit amount, in reserve token

Returns

Name	Type	Description
purchaseReturn	uint256	return amount

_calculateLinSaleReturn

Returns the sale value for a given amount (in the main token) as a conversion into the reserve token.

function _calculateLinSaleReturn(
    uint256 supply,
    uint256 reserveBalance,
    uint256 initialCost,
    uint32 scalingFactor,
    uint256 sellAmount
) internal pure returns (uint256 saleReturn);

Parameters

Name	Type	Description
supply	uint256	token total supply
reserveBalance	uint256	balance of the reserve token
initialCost	uint256	initial cost of the token
scalingFactor	uint32	scaling factor, represented in ppm, 1-1000000
sellAmount	uint256	amount of tokens to sell

Returns

Name	Type	Description
saleReturn	uint256	return of the conversion

_totalCostOfTokens

Returns the total cost of tokens up to the current token.

function _totalCostOfTokens(uint256 currentToken, uint32 scalingFactor, uint256 initialCost)
    internal
    pure
    returns (uint256 totalCost);

Parameters

Name	Type	Description
currentToken	uint256	current token number
scalingFactor	uint32	scaling factor, represented in ppm, 1-1000000
initialCost	uint256	initial cost of the token

Returns

Name	Type	Description
totalCost	uint256	total cost of tokens up to the current token

_currentTokenCost

Returns the cost of the current token.

function _currentTokenCost(uint256 currentToken, uint32 scalingFactor, uint256 initialCost)
    internal
    pure
    returns (uint256 currentTokenCost);

Parameters

Name	Type	Description
currentToken	uint256	current token number
scalingFactor	uint32	scaling factor, represented in ppm, 1-1000000
initialCost	uint256	initial cost of the token

Returns

Name	Type	Description
currentTokenCost	uint256	current token cost

_calculateInitialCostAdjustment

Returns the initial cost adjustment based on the scaling factor.

Calculates the difference between the initial cost and the incremental value applied to each token after the first.

function _calculateInitialCostAdjustment(uint256 initialCost, uint32 scalingFactor)
    internal
    pure
    returns (uint256 initialCostAdjustment);

Parameters

Name	Type	Description
initialCost	uint256	initial cost of the token
scalingFactor	uint32	scaling factor, represented in ppm, 1-1000000

Returns

Name	Type	Description
initialCostAdjustment	uint256	initial cost adjustment

_calculateTokenCount

Returns the amount of whole tokens the deposit can still cover.

function _calculateTokenCount(
    uint256 depositAmount,
    uint256 reserveBalance,
    uint256 initialCost,
    uint32 scalingFactor,
    uint256 currentToken
) internal pure returns (uint256 tokenCount);

Parameters

Name	Type	Description
depositAmount	uint256	deposit amount, in reserve token
reserveBalance	uint256	balance of the reserve token
initialCost	uint256	initial cost of the token
scalingFactor	uint32
currentToken	uint256	current token number

Returns

Name	Type	Description
tokenCount	uint256	amount of whole tokens the deposit can still cover

_generalSqrt

Returns the square root of a given value as proposed in EIP-7054.

function _generalSqrt(uint256 x) internal pure returns (uint128 z);

Parameters

Name	Type	Description
x	uint256	value to calculate the square root of

Returns

Name	Type	Description
z	uint128	square root of the value

_optimalSqrt

Returns the square root of a given value using the Babylonian method.

function _optimalSqrt(uint256 y) internal pure returns (uint256 z);

Parameters

Name	Type	Description
y	uint256	value to calculate the square root of

Returns

Name	Type	Description
z	uint256	square root of the value

_getLength

Returns the length of a given number.

function _getLength(uint256 x) internal pure returns (uint256 length);

Parameters

Name	Type	Description
x	uint256	number to calculate the length of

Returns

Name	Type	Description
length	uint256	length of the number

Errors

LinFormula__InvalidInput

error LinFormula__InvalidInput();