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.

Functions

• tryAdd(a, b)
• trySub(a, b)
• tryMul(a, b)
• tryDiv(a, b)
• tryMod(a, b)
• add(a, b)
• sub(a, b)
• mul(a, b)
• div(a, b)
• mod(a, b)
• sub(a, b, errorMessage)
• div(a, b, errorMessage)
• mod(a, b, errorMessage)

tryAdd(uint256 a, uint256 b) → bool, uint256 *internal*

Returns the addition of two unsigned integers, with an overflow flag.

Available since v3.4.

trySub(uint256 a, uint256 b) → bool, uint256 *internal*

Returns the substraction of two unsigned integers, with an overflow flag.

Available since v3.4.

tryMul(uint256 a, uint256 b) → bool, uint256 *internal*

Returns the multiplication of two unsigned integers, with an overflow flag.

Available since v3.4.

tryDiv(uint256 a, uint256 b) → bool, uint256 *internal*

Returns the division of two unsigned integers, with a division by zero flag.

Available since v3.4.

tryMod(uint256 a, uint256 b) → bool, uint256 *internal*

Returns the remainder of dividing two unsigned integers, with a division by zero flag.

Available since v3.4.

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, reverting 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), reverting 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.

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.

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

Returns the integer division of two unsigned integers, reverting 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, string errorMessage) → uint256 *internal*

Returns the remainder of dividing two unsigned integers. (unsigned integer modulo), reverting 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.

Functions

• mul(a, b)
• div(a, b)
• sub(a, b)
• add(a, b)

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.

sub(int256 a, int256 b) → int256 *internal*

Returns the subtraction of two signed integers, reverting on overflow.

Counterpart to Solidity’s - operator.

Requirements:

• Subtraction cannot overflow.

add(int256 a, int256 b) → int256 *internal*

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

Counterpart to Solidity’s + operator.

Requirements:

• Addition cannot overflow.

Math

Standard math utilities missing in the Solidity language.

Functions

• max(a, b)
• min(a, b)
• average(a, b)

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.