# Nat

Natural numbers with infinite precision.

Most operations on natural numbers (e.g. addition) are available as built-in operators (e.g. `1 + 1`). This module provides equivalent functions and `Text` conversion.

Import from the base library to use this module.

``import Nat "mo:base/Nat";``

## Type `Nat`​

``type Nat = Prim.Types.Nat``

Infinite precision natural numbers.

## Function `toText`​

``func toText(n : Nat) : Text``

Converts a natural number to its textual representation. Textual representation do not contain underscores to represent commas.

Example:

``Nat.toText 1234 // => "1234"``

## Function `fromText`​

``func fromText(text : Text) : ?Nat``

Creates a natural number from its textual representation. Returns `null` if the input is not a valid natural number.

Note: The textual representation must not contain underscores.

Example:

``Nat.fromText "1234" // => ?1234``

## Function `min`​

``func min(x : Nat, y : Nat) : Nat``

Returns the minimum of `x` and `y`.

Example:

``Nat.min(1, 2) // => 1``

## Function `max`​

``func max(x : Nat, y : Nat) : Nat``

Returns the maximum of `x` and `y`.

Example:

``Nat.max(1, 2) // => 2``

## Function `equal`​

``func equal(x : Nat, y : Nat) : Bool``

Equality function for Nat types. This is equivalent to `x == y`.

Example:

``ignore Nat.equal(1, 1); // => true1 == 1 // => true``

Note: The reason why this function is defined in this library (in addition to the existing `==` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `==` as a function value at the moment.

Example:

``import Buffer "mo:base/Buffer";let buffer1 = Buffer.Buffer<Nat>(3);let buffer2 = Buffer.Buffer<Nat>(3);Buffer.equal(buffer1, buffer2, Nat.equal) // => true``

## Function `notEqual`​

``func notEqual(x : Nat, y : Nat) : Bool``

Inequality function for Nat types. This is equivalent to `x != y`.

Example:

``ignore Nat.notEqual(1, 2); // => true1 != 2 // => true``

Note: The reason why this function is defined in this library (in addition to the existing `!=` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `!=` as a function value at the moment.

## Function `less`​

``func less(x : Nat, y : Nat) : Bool``

"Less than" function for Nat types. This is equivalent to `x < y`.

Example:

``ignore Nat.less(1, 2); // => true1 < 2 // => true``

Note: The reason why this function is defined in this library (in addition to the existing `<` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `<` as a function value at the moment.

## Function `lessOrEqual`​

``func lessOrEqual(x : Nat, y : Nat) : Bool``

"Less than or equal" function for Nat types. This is equivalent to `x <= y`.

Example:

``ignore Nat.lessOrEqual(1, 2); // => true1 <= 2 // => true``

Note: The reason why this function is defined in this library (in addition to the existing `<=` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `<=` as a function value at the moment.

## Function `greater`​

``func greater(x : Nat, y : Nat) : Bool``

"Greater than" function for Nat types. This is equivalent to `x > y`.

Example:

``ignore Nat.greater(2, 1); // => true2 > 1 // => true``

Note: The reason why this function is defined in this library (in addition to the existing `>` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `>` as a function value at the moment.

## Function `greaterOrEqual`​

``func greaterOrEqual(x : Nat, y : Nat) : Bool``

"Greater than or equal" function for Nat types. This is equivalent to `x >= y`.

Example:

``ignore Nat.greaterOrEqual(2, 1); // => true2 >= 1 // => true``

Note: The reason why this function is defined in this library (in addition to the existing `>=` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `>=` as a function value at the moment.

## Function `compare`​

``func compare(x : Nat, y : Nat) : {#less; #equal; #greater}``

General purpose comparison function for `Nat`. Returns the `Order` ( either `#less`, `#equal`, or `#greater`) of comparing `x` with `y`.

Example:

``Nat.compare(2, 3) // => #less``

This function can be used as value for a high order function, such as a sort function.

Example:

``import Array "mo:base/Array";Array.sort([2, 3, 1], Nat.compare) // => [1, 2, 3]``

## Function `add`​

``func add(x : Nat, y : Nat) : Nat``

Returns the sum of `x` and `y`, `x + y`. This operator will never overflow because `Nat` is infinite precision.

Example:

``ignore Nat.add(1, 2); // => 31 + 2 // => 3``

Note: The reason why this function is defined in this library (in addition to the existing `+` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `+` as a function value at the moment.

Example:

``import Array "mo:base/Array";Array.foldLeft([2, 3, 1], 0, Nat.add) // => 6``

## Function `sub`​

``func sub(x : Nat, y : Nat) : Nat``

Returns the difference of `x` and `y`, `x - y`. Traps on underflow below `0`.

Example:

``ignore Nat.sub(2, 1); // => 1// Add a type annotation to avoid a warning about the subtraction2 - 1 : Nat // => 1``

Note: The reason why this function is defined in this library (in addition to the existing `-` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `-` as a function value at the moment.

Example:

``import Array "mo:base/Array";Array.foldLeft([2, 3, 1], 10, Nat.sub) // => 4``

## Function `mul`​

``func mul(x : Nat, y : Nat) : Nat``

Returns the product of `x` and `y`, `x * y`. This operator will never overflow because `Nat` is infinite precision.

Example:

``ignore Nat.mul(2, 3); // => 62 * 3 // => 6``

Note: The reason why this function is defined in this library (in addition to the existing `*` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `*` as a function value at the moment.

Example:

``import Array "mo:base/Array";Array.foldLeft([2, 3, 1], 1, Nat.mul) // => 6``

## Function `div`​

``func div(x : Nat, y : Nat) : Nat``

Returns the unsigned integer division of `x` by `y`, `x / y`. Traps when `y` is zero.

The quotient is rounded down, which is equivalent to truncating the decimal places of the quotient.

Example:

``ignore Nat.div(6, 2); // => 36 / 2 // => 3``

Note: The reason why this function is defined in this library (in addition to the existing `/` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `/` as a function value at the moment.

## Function `rem`​

``func rem(x : Nat, y : Nat) : Nat``

Returns the remainder of unsigned integer division of `x` by `y`, `x % y`. Traps when `y` is zero.

Example:

``ignore Nat.rem(6, 4); // => 26 % 4 // => 2``

Note: The reason why this function is defined in this library (in addition to the existing `%` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `%` as a function value at the moment.

## Function `pow`​

``func pow(x : Nat, y : Nat) : Nat``

Returns `x` to the power of `y`, `x ** y`. Traps when `y > 2^32`. This operator will never overflow because `Nat` is infinite precision.

Example:

``ignore Nat.pow(2, 3); // => 82 ** 3 // => 8``

Note: The reason why this function is defined in this library (in addition to the existing `**` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `**` as a function value at the moment.