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Numbers

Natural numbers​

The Nat type represents natural numbers, which are all non-negative integers (i.e., 0 and positive numbers).

let n : Nat = 42;
let zero : Nat = 0;

Defining a Nat with a negative value is a compile time error:

let negative : Nat = -1; // Error: Cannot assign a negative value to Nat

Unbounded natural numbers​

Like Int, the Nat type is unbounded by default, allowing extremely large values without overflow.

let hugeNat : Nat = 1_000_000_000_000_000;

Bounded natural numbers​

Motoko also provides bounded natural number types.

  • Nat8 (8-bit unsigned integer, range: 0 to 255)
  • Nat16 (16-bit unsigned integer, range: 0 to 65,535)
  • Nat32 (32-bit unsigned integer, range: 0 to 4,294,967,295)
  • Nat64 (64-bit unsigned integer, range: 0 to 18,446,744,073,709,551,615)

Bounded Nat types are ideal when working with binary protocols, embedded systems, or hardware where size constraints matter.

let trappingNat8 : Nat8 = 255+1; // trap: arithmetic overflow

Integers​

Int represents all integers, both positive and negative (e.g., -2, -1, 0, 1, 2).

For scenarios requiring fixed-size integers, Motoko offers bounded variants with specific bit-widths (Int8, Int16, Int32, Int64). These types can overflow if their limits are exceeded, resulting in a runtime error.

let a : Int = -42;
let b : Int = 0;
let c : Int = 12345;

Unbounded integers​

The Int is unbounded, meaning its values can grow as large (or as small) as needed without causing over- or underflow.

let bigNumber : Int = 999_999_999_999_999;

Bounded integers​

  • Int8 (8-bit signed integer)
  • Int16 (16-bit signed integer)
  • Int32 (32-bit signed integer)
  • Int64 (64-bit signed integer)

Arithmetic on bounded integers can overflow if their limits are exceeded, resulting in a runtime error.

let trappingInt8 : Int8 = 127+1; // trap: arithmetic overflow

Comparing Int and Nat​

FeatureIntNat
Values supportedPositive & negativeOnly non-negative
Default behaviorUnboundedUnbounded
Bounded variantsInt8, Int16, Int32...Nat8, Nat16, Nat32...
Overflow possibilityYes (for bounded types)Yes (for bounded types)

Floats​

Floating-point numbers in Motoko are represented using the Float type, which corresponds to a 64-bit double-precision floating-point number in IEEE 754 representation.

Limited precision

Floating point numbers have limited precision and operations may inherently result in numerical errors.

let pi : Float = 3.14159;
let exp : Float = 2.71828;
let goldenRatio = 1.61803;

Resources​

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