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.

`add(uint256 a, uint256 b, string errorMessage) → uint256`

(internal)Returns the addition of two unsigned integers, reverting with custom message 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 underflow (when the result is negative). Counterpart to Solidity's

`-`

operator. Requirements:- Subtraction cannot underflow.

`sub(uint256 a, uint256 b, string errorMessage) → uint256`

(internal)Returns the subtraction of two unsigned integers, reverting with custom message on underflow (when the result is negative). Counterpart to Solidity's

`-`

operator. Requirements:- Subtraction cannot underflow.

`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.

`mul(uint256 a, uint256 b, string errorMessage) → 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.

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add(uint256 a, uint256 b) → uint256 (internal)

add(uint256 a, uint256 b, string errorMessage) → uint256 (internal)

sub(uint256 a, uint256 b) → uint256 (internal)

sub(uint256 a, uint256 b, string errorMessage) → uint256 (internal)

mul(uint256 a, uint256 b) → uint256 (internal)

mul(uint256 a, uint256 b, string errorMessage) → uint256 (internal)

div(uint256 a, uint256 b) → uint256 (internal)

div(uint256 a, uint256 b, string errorMessage) → uint256 (internal)

mod(uint256 a, uint256 b) → uint256 (internal)

mod(uint256 a, uint256 b, string errorMessage) → uint256 (internal)