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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); // => true
1 == 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); // => true
1 != 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); // => true
1 < 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); // => true
1 <= 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); // => true
2 > 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); // => true
2 >= 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); // => 3
1 + 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 subtraction
2 - 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); // => 6
2 * 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); // => 3
6 / 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); // => 2
6 % 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); // => 8
2 ** 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.

Function bitshiftLeft​

func bitshiftLeft(x : Nat, y : Nat32) : Nat

Returns the (conceptual) bitwise shift left of x by y, x * (2 ** y).

Example:

Nat.bitshiftLeft(1, 3); // => 8

Note: The reason why this function is defined in this library (in absence of the << operator) is so that you can use it as a function value to pass to a higher order function. While Nat is not defined in terms of bit patterns, conceptually it can be regarded as such, and the operation is provided as a high-performance version of the corresponding arithmetic rule.

Function bitshiftRight​

func bitshiftRight(x : Nat, y : Nat32) : Nat

Returns the (conceptual) bitwise shift right of x by y, x / (2 ** y).

Example:

Nat.bitshiftRight(8, 3); // => 1

Note: The reason why this function is defined in this library (in absence of the >> operator) is so that you can use it as a function value to pass to a higher order function. While Nat is not defined in terms of bit patterns, conceptually it can be regarded as such, and the operation is provided as a high-performance version of the corresponding arithmetic rule.