ABDKMath64x64

The ABDKMath64x64 library provides fixed-point arithmetic operations.

mulu

Calculate x * y rounding down, where x is a signed 64.64 fixed-point number, and y is an unsigned 256-bit integer. Revert on overflow.

function mulu (
    int128 x, 
    uint256 y) internal pure returns (uint256)

Parameters:

Name	Type	Description
x	int128	Signed 64.64 fixed-point number.
y	uint	Unsigned 256-bit integer.

Return Values:

Name	Type	Description
None	uint	Unsigned 256-bit integer.

divu

Calculate x / y rounding towards zero, where x and y are unsigned 256-bit integer numbers. Revert on overflow or when y is zero.

function divu (
    uint256 x, 
    uint256 y) internal pure returns (int128)

Parameters:

Name	Type	Description
x	uint	Unsigned 256-bit integer.
y	uint	Unsigned 256-bit integer.

Return Values:

Name	Type	Description
None	int128	Signed 64.64 fixed-point number.

exp_2

The exp_2 function calculates the binary exponent of a given signed 64.64-bit fixed-point number, x. This function utilizes a series of conditional multiplications based on the bits set in the binary representation of x. The purpose is to efficiently approximate the value of 2^x without resorting to iterative calculations, ensuring that the result is a signed 64.64-bit fixed-point number.

function exp_2 (
    int128 x) internal pure returns (int128)

Parameters:

Name	Type	Description
x	int128	Signed 64.64 fixed-point number.

Return Values:

Name	Type	Description
None	int128	Signed 64.64 fixed-point number.

divuu

Internal function to calculate x / y rounding towards zero, where x and y are unsigned 256-bit integer numbers. Revert on overflow or when y is zero.

This function is designed to provide a robust and efficient method for dividing two uint256 numbers in a way that accounts for various scenarios, including large numbers and potential overflow issues. The approach combines bit manipulation, conditional statements, and explicit checks to balance performance and accuracy.

function divuu (
    uint256 x, 
    uint256 y) private pure returns (uint128)

Parameters:

Name	Type	Description
x	uint	Unsigned 256-bit integer.
y	uint	Unsigned 256-bit integer.

Return Values:

Name	Type	Description
None	uint128	Unsigned 64.64 fixed-point number.

This library plays a pivotal role in Dyson Finance, notably in the divu and exp_2 functions, which are extensively employed. These functions are integral to several critical calculations within various contracts:

// Farm.sol
function _calcRewardAmount(uint _reserve, uint _amount, uint _w) internal pure returns (uint reward)

// Pair.sol
function calcNewFeeRatio(uint64 _oldFeeRatio, uint _elapsedTime) public view returns (uint64 _newFeeRatio)

// sDYSON.sol
function stakingRate(uint lockDuration) external view returns (uint rate)