The following is the documentation for binary arithmetic operators. The binary arithmetic operators are of the form: `x = a <operator> b`

or `x = <operator name>(a, b)`

.

The documentation includes references to exceptions and relaxations.

For more information on exceptions, see exceptions.

For more information on relaxations, see relaxations.

## Mathematics of Fixed Precision

All operations result in a decimal number type with 15 digits. The mathematics of this is covered in the section on the Decimal Number Type.

## Operators

### Addition

Syntax: `x = a + b`

Description: Sets x to the sum of a and b.

Exceptions:

- Overflow

Relaxations:

- Binary
- Exception

### Subtraction

Syntax: `x = a - b`

Description: Sets x to the difference between a and b.

Exceptions:

- Overflow

Relaxations:

- Binary
- Exception

### Multiplication

Syntax: `x = a * b`

Description: Sets x to the product of a and b.

Exceptions:

- Overflow

Relaxations:

- Binary
- Exception

### Division

Syntax: `x = a / b`

Description: Sets x to a divided by b.

Exceptions:

- Overflow
- Invalid operand, if b is zero.

Relaxations:

- Binary
- Exception

### Exponentiation

Syntax: `x = a ^ b`

Description: Sets x to a to the power of b.

Exceptions:

- Overflow
- Invalid operand
- If both a and b are zero.
- If a is negative and b is not a whole number.

Relaxations:

- Binary
- Exception

### Modulus

Syntax: `x = a mod b`

Description: Sets x to the reminder of a divided by b with integer division. The result is `0 <= x < b`

. Another way at looking at it is that `x = a - q*b`

, where q is the integer quotient when a is divided by b using integer division.

Exceptions:

- Invalid operand
- If a is negative.
- If b is zero.
- If b is negative.

Relaxations:

- Binary
- Exception

### Max

Syntax: `x = max(a, b)`

Description: x is the larger of a and b.

### Min

Syntax: `x = min(a, b)`

Description: x is the smaller of a and b,