FullMath

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

Handles "phantom overflow" and prevents overflow of 256 bits in intermediate values between the multiplication and division steps.

Functions

safeMulDiv

  function safeMulDiv(
    uint256 value,
    uint256 multiplier,
    uint256 denominator
  ) internal pure returns (uint256 result)

Calculates floor(value×multiplier÷denominator) with maximum precision. Reverts 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
value	uint256	The multiplicand
multiplier	uint256	The multiplier
denominator	uint256	The divisor

Return Values:

Name	Type	Description
result	uint256	The 256-bit result

safeMulDivCeiling

  function safeMulDivCeiling(
    uint256 initial,
    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
value	uint256	The multiplicand
multiplier	uint256	The multiplier
denominator	uint256	The divisor

Return Values:

Name	Type	Description
result	uint256	The 256-bit result