FullMath

Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision

Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits

Functions

mulDiv

  function mulDiv(
    uint256 a,
    uint256 b,
    uint256 denominator
  ) internal pure returns (uint256 result)

Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0

Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv

Parameters:

Name	Type	Description
a	uint256	The multiplicand
b	uint256	The multiplier
denominator	uint256	The divisor

Return Values:

Name	Type	Description
result	uint256	The 256-bit result

mulDivRoundingUp

  function mulDivRoundingUp(
    uint256 a,
    uint256 b,
    uint256 denominator
  ) internal pure returns (uint256 result)

Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0

Parameters:

Name	Type	Description
a	uint256	The multiplicand
b	uint256	The multiplier
denominator	uint256	The divisor

Return Values:

Name	Type	Description
result	uint256	The 256-bit result