# Math

These are math-related utilities.

## Libraries

`SafeMath`

Wrappers over Solidity's arithmetic operations with added overflow checks.

Arithmetic operations in Solidity wrap on overflow. This can easily result
in bugs, because programmers usually assume that an overflow raises an
error, which is the standard behavior in high level programming languages.
`SafeMath`

restores this intuition by reverting the transaction when an
operation overflows.

Using this library instead of the unchecked operations eliminates an entire class of bugs, so it's recommended to use it always.

`add(uint256 a, uint256 b) → uint256`

internal

Returns the addition of two unsigned integers, reverting on overflow.

Counterpart to Solidity's `+`

operator.

Requirements:

- Addition cannot overflow.

`sub(uint256 a, uint256 b) → uint256`

internal

Returns the subtraction of two unsigned integers, reverting on overflow (when the result is negative).

Counterpart to Solidity's `-`

operator.

Requirements:

- Subtraction cannot overflow.

`mul(uint256 a, uint256 b) → uint256`

internal

Returns the multiplication of two unsigned integers, reverting on overflow.

Counterpart to Solidity's `*`

operator.

Requirements:

- Multiplication cannot overflow.

`div(uint256 a, uint256 b) → uint256`

internal

Returns the integer division of two unsigned integers. Reverts on division by zero. The result is rounded towards zero.

Counterpart to Solidity's `/`

operator. Note: this function uses a
`revert`

opcode (which leaves remaining gas untouched) while Solidity
uses an invalid opcode to revert (consuming all remaining gas).

Requirements:

- The divisor cannot be zero.

`mod(uint256 a, uint256 b) → uint256`

internal

Returns the remainder of dividing two unsigned integers. (unsigned integer modulo), Reverts when dividing by zero.

Counterpart to Solidity's `%`

operator. This function uses a `revert`

opcode (which leaves remaining gas untouched) while Solidity uses an
invalid opcode to revert (consuming all remaining gas).

Requirements:

- The divisor cannot be zero.

`Math`

Standard math utilities missing in the Solidity language.

`max(uint256 a, uint256 b) → uint256`

internal

Returns the largest of two numbers.

`min(uint256 a, uint256 b) → uint256`

internal

Returns the smallest of two numbers.

`average(uint256 a, uint256 b) → uint256`

internal

Returns the average of two numbers. The result is rounded towards zero.