Uint256x256Math

Git Source

Author:
Trader Joe

Helper contract used for full precision calculations

Functions

mulDivRoundDown

Calculates floor(x*y/denominator) with full precision
The result will be rounded down

*Credit to Remco Bloemen under MIT license https://2π.com/21/muldiv\\ Requirements:

• The denominator cannot be zero
• The result must fit within uint256
  Caveats:
• This function does not work with fixed-point numbers*

function mulDivRoundDown(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result);

Parameters

Name	Type	Description
x	uint256	The multiplicand as an uint256
y	uint256	The multiplier as an uint256
denominator	uint256	The divisor as an uint256

Returns

Name	Type	Description
result	uint256	The result as an uint256

mulDivRoundUp

Calculates ceil(x*y/denominator) with full precision
The result will be rounded up

*Credit to Remco Bloemen under MIT license https://2π.com/21/muldiv\\ Requirements:

• The denominator cannot be zero
• The result must fit within uint256
  Caveats:
• This function does not work with fixed-point numbers*

function mulDivRoundUp(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result);

Parameters

Name	Type	Description
x	uint256	The multiplicand as an uint256
y	uint256	The multiplier as an uint256
denominator	uint256	The divisor as an uint256

Returns

Name	Type	Description
result	uint256	The result as an uint256

mulShiftRoundDown

Calculates floor(x * y / 2**offset) with full precision
The result will be rounded down

*Credit to Remco Bloemen under MIT license https://2π.com/21/muldiv\\ Requirements:

• The offset needs to be strictly lower than 256
• The result must fit within uint256
  Caveats:
• This function does not work with fixed-point numbers*

function mulShiftRoundDown(uint256 x, uint256 y, uint8 offset) internal pure returns (uint256 result);

Parameters

Name	Type	Description
x	uint256	The multiplicand as an uint256
y	uint256	The multiplier as an uint256
offset	uint8	The offset as an uint256, can't be greater than 256

Returns

Name	Type	Description
result	uint256	The result as an uint256

mulShiftRoundUp

Calculates floor(x * y / 2**offset) with full precision
The result will be rounded down

*Credit to Remco Bloemen under MIT license https://2π.com/21/muldiv\\ Requirements:

• The offset needs to be strictly lower than 256
• The result must fit within uint256
  Caveats:
• This function does not work with fixed-point numbers*

function mulShiftRoundUp(uint256 x, uint256 y, uint8 offset) internal pure returns (uint256 result);

Parameters

Name	Type	Description
x	uint256	The multiplicand as an uint256
y	uint256	The multiplier as an uint256
offset	uint8	The offset as an uint256, can't be greater than 256

Returns

Name	Type	Description
result	uint256	The result as an uint256

shiftDivRoundDown

Calculates floor(x << offset / y) with full precision
The result will be rounded down

*Credit to Remco Bloemen under MIT license https://2π.com/21/muldiv\\ Requirements:

• The offset needs to be strictly lower than 256
• The result must fit within uint256
  Caveats:
• This function does not work with fixed-point numbers*

function shiftDivRoundDown(uint256 x, uint8 offset, uint256 denominator) internal pure returns (uint256 result);

Parameters

Name	Type	Description
x	uint256	The multiplicand as an uint256
offset	uint8	The number of bit to shift x as an uint256
denominator	uint256	The divisor as an uint256

Returns

Name	Type	Description
result	uint256	The result as an uint256

shiftDivRoundUp

Calculates ceil(x << offset / y) with full precision
The result will be rounded up

*Credit to Remco Bloemen under MIT license https://2π.com/21/muldiv\\ Requirements:

• The offset needs to be strictly lower than 256
• The result must fit within uint256
  Caveats:
• This function does not work with fixed-point numbers*

function shiftDivRoundUp(uint256 x, uint8 offset, uint256 denominator) internal pure returns (uint256 result);

Parameters

Name	Type	Description
x	uint256	The multiplicand as an uint256
offset	uint8	The number of bit to shift x as an uint256
denominator	uint256	The divisor as an uint256

Returns

Name	Type	Description
result	uint256	The result as an uint256

_getMulProds

Helper function to return the result of x * y as 2 uint256

function _getMulProds(uint256 x, uint256 y) private pure returns (uint256 prod0, uint256 prod1);

Parameters

Name	Type	Description
x	uint256	The multiplicand as an uint256
y	uint256	The multiplier as an uint256

Returns

Name	Type	Description
prod0	uint256	The least significant 256 bits of the product
prod1	uint256	The most significant 256 bits of the product

_getEndOfDivRoundDown

Helper function to return the result of x * y / denominator with full precision

function _getEndOfDivRoundDown(uint256 x, uint256 y, uint256 denominator, uint256 prod0, uint256 prod1)
    private
    pure
    returns (uint256 result);

Parameters

Name	Type	Description
x	uint256	The multiplicand as an uint256
y	uint256	The multiplier as an uint256
denominator	uint256	The divisor as an uint256
prod0	uint256	The least significant 256 bits of the product
prod1	uint256	The most significant 256 bits of the product

Returns

Name	Type	Description
result	uint256	The result as an uint256

sqrt

Calculates the square root of x

Credit to OpenZeppelin's Math library under MIT license

function sqrt(uint256 x) internal pure returns (uint256 sqrtX);

Errors

Uint256x256Math__MulShiftOverflow

error Uint256x256Math__MulShiftOverflow();

Uint256x256Math__MulDivOverflow

error Uint256x256Math__MulDivOverflow();