# Arithmetic Operators

This topic describes arithmetic operators that are available in the F# language.

## Summary of Binary Arithmetic Operators

The following table summarizes the binary arithmetic operators that are available for unboxed integral and floating-point types.

Binary operator Notes
+ (addition, plus) Unchecked. Possible overflow condition when numbers are added together and the sum exceeds the maximum absolute value supported by the type.
- (subtraction, minus) Unchecked. Possible underflow condition when unsigned types are subtracted, or when floating-point values are too small to be represented by the type.
* (multiplication, times) Unchecked. Possible overflow condition when numbers are multiplied and the product exceeds the maximum absolute value supported by the type.
/ (division, divided by) Division by zero causes a DivideByZeroException for integral types. For floating-point types, division by zero gives you the special floating-point values +Infinity or -Infinity. There is also a possible underflow condition when a floating-point number is too small to be represented by the type.
% (remainder, rem) Returns the remainder of a division operation. The sign of the result is the same as the sign of the first operand.
** (exponentiation, to the power of) Possible overflow condition when the result exceeds the maximum absolute value for the type.

The exponentiation operator works only with floating-point types.

## Summary of Unary Arithmetic Operators

The following table summarizes the unary arithmetic operators that are available for integral and floating-point types.

Unary operator Notes
+ (positive) Can be applied to any arithmetic expression. Does not change the sign of the value.
- (negation, negative) Can be applied to any arithmetic expression. Changes the sign of the value.

The behavior at overflow or underflow for integral types is to wrap around. This causes an incorrect result. Integer overflow is a potentially serious problem that can contribute to security issues when software is not written to account for it. If this is a concern for your application, consider using the checked operators in Microsoft.FSharp.Core.Operators.Checked.

## Summary of Binary Comparison Operators

The following table shows the binary comparison operators that are available for integral and floating-point types. These operators return values of type bool.

Floating-point numbers should never be directly compared for equality, because the IEEE floating-point representation does not support an exact equality operation. Two numbers that you can easily verify to be equal by inspecting the code might actually have different bit representations.

Operator Notes
= (equality, equals) This is not an assignment operator. It is used only for comparison. This is a generic operator.
> (greater than) This is a generic operator.
< (less than) This is a generic operator.
>= (greater than or equals) This is a generic operator.
<= (less than or equals) This is a generic operator.
<> (not equal) This is a generic operator.

All of the operators discussed in this topic are defined in the Microsoft.FSharp.Core.Operators namespace. Some of the operators are defined by using statically resolved type parameters. This means that there are individual definitions for each specific type that works with that operator. All of the unary and binary arithmetic and bitwise operators are in this category. The comparison operators are generic and therefore work with any type, not just primitive arithmetic types. Discriminated union and record types have their own custom implementations that are generated by the F# compiler. Class types use the method Equals.

The generic operators are customizable. To customize the comparison functions, override Equals to provide your own custom equality comparison, and then implement IComparable. The System.IComparable interface has a single method, the CompareTo method.

## Operators and Type Inference

The use of an operator in an expression constrains type inference on that operator. Also, the use of operators prevents automatic generalization, because the use of operators implies an arithmetic type. In the absence of any other information, the F# compiler infers int as the type of arithmetic expressions. You can override this behavior by specifying another type. Thus the argument types and return type of function1 in the following code are inferred to be int, but the types for function2 are inferred to be float.

// x, y and return value inferred to be int
// function1: int -> int -> int
let function1 x y = x + y

// x, y and return value inferred to be float
// function2: float -> float -> float
let function2 (x: float) y = x + y