Math
These are mathrelated 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.
sub(uint256 a, uint256 b, string errorMessage) → uint256
internal
Returns the subtraction of two unsigned integers, reverting with custom message 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.
div(uint256 a, uint256 b, string errorMessage) → uint256
internal
Returns the integer division of two unsigned integers. Reverts with custom message 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.
mod(uint256 a, uint256 b, string errorMessage) → uint256
internal
Returns the remainder of dividing two unsigned integers. (unsigned integer modulo), Reverts with custom message 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.
SignedSafeMath
Signed math operations with safety checks that revert on error.
mul(int256 a, int256 b) → int256
internal
Returns the multiplication of two signed integers, reverting on overflow.
Counterpart to Solidity’s *
operator.
Requirements:

Multiplication cannot overflow.
div(int256 a, int256 b) → int256
internal
Returns the integer division of two signed 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.