# Operations

## Table of Supported Operations

Operation | Description | Requirements |
---|---|---|

+ | Adds two private input types together | Types must be private input |

- | Subtracts two private input types together | Types must be private input |

* | Multiplies two private input types together | Types must be private input |

/ | Divides two private input types together | Types must be private input |

^ | XOR two private input types together | Types must be integer |

& | AND two private input types together | Types must be integer |

| | OR two private input types together | Types must be integer |

<< | Left shift an integer by another integer amount | Types must be integer, shift must be u8 |

>> | Right shift an integer by another integer amount | Types must be integer, shift must be u8 |

! | Bitwise not of a value | Type must be integer or boolean |

< | returns a bool if one value is less than the other | Upper bound must have a known bit size |

<= | returns a bool if one value is less than or equal to the other | Upper bound must have a known bit size |

> | returns a bool if one value is more than the other | Upper bound must have a known bit size |

>= | returns a bool if one value is more than or equal to the other | Upper bound must have a known bit size |

== | returns a bool if one value is equal to the other | Both types must not be constants |

!= | returns a bool if one value is not equal to the other | Both types must not be constants |

### Predicate Operators

`<,<=, !=, == , >, >=`

are known as predicate/comparison operations because they compare two values.
This differs from the operations such as `+`

where the operands are used in *computation*.

### Bitwise Operations Example

`fn main(x : Field) {`

let y = x as u32;

let z = y & y;

}

`z`

is implicitly constrained to be the result of `y & y`

. The `&`

operand is used to denote bitwise
`&`

.

`x & x`

would not compile as`x`

is a`Field`

and not an integer type.

### Logical Operators

Noir has no support for the logical operators `||`

and `&&`

. This is because encoding the
short-circuiting that these operators require can be inefficient for Noir's backend. Instead you can
use the bitwise operators `|`

and `&`

which operate identically for booleans, just without the
short-circuiting.

`let my_val = 5;`

let mut flag = 1;

if (my_val > 6) | (my_val == 0) {

flag = 0;

}

assert(flag == 1);

if (my_val != 10) & (my_val < 50) {

flag = 0;

}

assert(flag == 0);

### Shorthand operators

Noir shorthand operators for most of the above operators, namely `+=, -=, *=, /=, %=, &=, |=, ^=, <<=`

, and `>>=`

. These allow for more concise syntax. For example:

`let mut i = 0;`

i = i + 1;

could be written as:

`let mut i = 0;`

i += 1;